New Geometry of Quantum Dynamics

Risultati finali

Dissemination: NCG seminar (Trimming and growing of graphs for graph algebras)

D2 seminars and talks are the second tangible deliverable related to scientific output: we shall continuously collect recordings of the NCG Seminar at IMPAN as well as either slides or recordings from other seminars by the members of the team – and summarize them on a yearly basis (M12, M24, M36, M48) to monitor the dissemination. All deliverables of this type shall be available on the Web page and/or youtube channel.

Dissemination: NCG seminar (Noncommutative spectral geometry for quantum group homogeneous spaces)

Focus programme (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

D7 Focus Program at the Fields Insttute – is expected to be the final and summarising event of the project, the deliverable will be talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).

Simons Semester at the Banach Center (Noncommutative bordism of quantum fibrations)

D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/ seminars during the event (in a form of the web page).

Proceedings (Trimming and growing of graphs for graph algebras)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Special issue (Noncommutative spectral geometry for quantum group homogeneous spaces)

D8 Special issue of SIGMA: Special issue of Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) on New Geometry of Quantum Dynamics will be a closing volume summarising scientific achievements of the project with submitted papers by majority (if not all) participants.

Focus programme (Trimming and growing of graphs for graph algebras)

Special issue (Trimming and growing of graphs for graph algebras)

Research papers (Noncommutative bordism of quantum fibrations)

D1 research papers are the crucial deliverable, which monitors the scientific output of the project and the progress in the realisation of the project as well as the effectiveness of the collaborations. Since papers will be made available irregularly we shall update the information on them continuously, however, to effectively monitor the outcome we shall summarize the publications and collect them on a yearly basis (M12, M24, M36, M48). Deliverable shall be made available and through Arxives/web page.

Simons Semester at the Banach Center (Trimming and growing of graphs for graph algebras)

Special issue (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Proceedings (Noncommutative bordism of quantum fibrations)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Research papers (Noncommutative Borsuk–Ulam-type conjectures)

Focus programme (Noncommutative spectral geometry for quantum group homogeneous spaces)

Research papers (Trimming and growing of graphs for graph algebras)

Dissemination: NCG seminar (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Proceedings (Noncommutative spectral geometry for quantum group homogeneous spaces)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Research papers (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Simons Semester at the Banach Center (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

Proceedings (Noncommutative metric geometry of C*-dynamical systems and graph C*-algebras)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Research papers (Noncommutative spectral geometry for quantum group homogeneous spaces)

Special issue (Noncommutative Borsuk–Ulam-type conjectures)

Focus programme (Noncommutative bordism of quantum fibrations)

Focus programme (Noncommutative Borsuk–Ulam-type conjectures)

Proceedings (Noncommutative Borsuk–Ulam-type conjectures)

D6 Proceedings: Banach Center Proceedings of the planned Simons Semester at IMPAN, Noncommutative geometry the next generation will contain the research papers submitted to the volume.

Dissemination: NCG seminar (Noncommutative Borsuk–Ulam-type conjectures)

Simons Semester at the Banach Center (Noncommutative Borsuk–Ulam-type conjectures)

Special issue (Noncommutative bordism of quantum fibrations)

Dissemination: NCG seminar (Noncommutative bordism of quantum fibrations)

Simons Semester at the Banach Center (Noncommutative spectral geometry for quantum group homogeneous spaces)

D5 Simons Semester at the Banach Center: network-wide event planned at the Banach center, the deliverable will comprise talks (recorded and slides)/abstracts of lectures/seminars during the event (in a form of the web page).

Dedicated Web page (Management)

D3 dedicated Web page shall be created at the beginning of the project and updated on a continuous basis: page will hold all information pertaining to the project: about secondments, dissemination (publications, preprints, talks, seminars) and events which involve and/or are related to the project. The internal section of the web page (which includes internal reports) shall be available to project team.

Progress report (Management)

Progress report will summarize the scientific achievements, secondments, dissemination and commmunication (outreach activities) by the participants. Deliverable shall be archived/stored at IMPAN, electronic vesions shall be available on the Web page.

Progress report 2 (Management)

Pubblicazioni

Continuity of spectral radius and type I $C^*$-algebras

Autori: Tatiana Shulman
Pubblicato in: Proceedings of the American Mathematical Society, Numero 147/2, 2019, Pagina/e 641-646, ISSN 0002-9939
Editore: American Mathematical Society
DOI: 10.1090/proc/14169

Quantum actions on discrete quantum spaces and a generalization of Clifford’s theory of representations

Autori: Kenny De Commer, Paweł Kasprzak, Adam Skalski, Piotr M. Sołtan
Pubblicato in: Israel Journal of Mathematics, Numero 226/1, 2018, Pagina/e 475-503, ISSN 0021-2172
Editore: Magnes Press
DOI: 10.1007/s11856-018-1709-x

I-factorial quantum torsors and Heisenberg algebras of quantized universal enveloping type

Autori: Kenny De Commer
Pubblicato in: Journal of Functional Analysis, Numero 274/1, 2018, Pagina/e 152-221, ISSN 0022-1236
Editore: Academic Press
DOI: 10.1016/j.jfa.2017.09.005

Partial actions of $C^{*}$ -quantum groups

Autori: Franziska Kraken, Paula Quast, Thomas Timmermann
Pubblicato in: Banach Journal of Mathematical Analysis, Numero 12/4, 2018, Pagina/e 843-872, ISSN 1735-8787
Editore: Banach Mathematical Research Group
DOI: 10.1215/17358787-2017-0056

Ribbon Braided Module Categories, Quantum Symmetric Pairs and Knizhnik–Zamolodchikov Equations

Autori: Kenny De Commer, Sergey Neshveyev, Lars Tuset, Makoto Yamashita
Pubblicato in: Communications in Mathematical Physics, Numero 367/3, 2019, Pagina/e 717-769, ISSN 0010-3616
Editore: Springer Verlag
DOI: 10.1007/s00220-019-03317-7

Free products with amalgamation over central $\mathrm {C}^*$-subalgebras

Autori: Kristin Courtney, Tatiana Shulman
Pubblicato in: Proceedings of the American Mathematical Society, Numero 148/2, 2020, Pagina/e 765-776, ISSN 0002-9939
Editore: American Mathematical Society
DOI: 10.1090/proc/14746

The field of quantum $$GL(N,\pmb {\mathbb {C}})$$ G L ( N , C )

Autori: Kenny De Commer, Matthias Floré
Pubblicato in: Selecta Mathematica, Numero 25/1, 2019, ISSN 1022-1824
Editore: Birkhauser Verlag
DOI: 10.1007/s00029-019-0456-0

Geometric Classification of Graph C*-algebras over Finite Graphs

Autori: Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P.W. Sørensen
Pubblicato in: Canadian Journal of Mathematics, Numero 70/2, 2018, Pagina/e 294-353, ISSN 0008-414X
Editore: Canadian Mathematical Society
DOI: 10.4153/cjm-2017-016-7

A dynamical characterization of diagonal-preserving -isomorphisms of graph -algebras

Autori: SARA E. ARKLINT, SØREN EILERS, EFREN RUIZ
Pubblicato in: Ergodic Theory and Dynamical Systems, Numero 38/7, 2018, Pagina/e 2401-2421, ISSN 0143-3857
Editore: Cambridge University Press
DOI: 10.1017/etds.2016.141

Projective Modules Over Quantum Projective Line

Autori: Albert Jeu-Liang Sheu
Pubblicato in: International Journal of Mathematics, Numero 28/03, 2017, Pagina/e 1750022, ISSN 0129-167X
Editore: World Scientific Publishing Co
DOI: 10.1142/s0129167x17500227

Representations of higher-rank graph C⁎-algebras associated to Λ-semibranching function systems

Autori: Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen, Sooran Kang, Judith Packer
Pubblicato in: Journal of Mathematical Analysis and Applications, Numero 468/2, 2018, Pagina/e 766-798, ISSN 0022-247X
Editore: Academic Press
DOI: 10.1016/j.jmaa.2018.08.051

Projections over quantum homogeneous odd-dimensional spheres

Autori: Albert Jeu-Liang Sheu
Pubblicato in: Journal of Functional Analysis, Numero 277/10, 2019, Pagina/e 3491-3512, ISSN 0022-1236
Editore: Academic Press
DOI: 10.1016/j.jfa.2019.05.006

Noncommutative solenoids and the Gromov-Hausdorff propinquity

Autori: Frédéric Latrémolière, Judith Packer
Pubblicato in: Proceedings of the American Mathematical Society, Numero 145/5, 2017, Pagina/e 2043-2057, ISSN 0002-9939
Editore: American Mathematical Society
DOI: 10.1090/proc/13229

Equivalence of quantum metrics with a common domain

Autori: Frédéric Latrémolière
Pubblicato in: Journal of Mathematical Analysis and Applications, Numero 443/2, 2016, Pagina/e 1179-1195, ISSN 0022-247X
Editore: Academic Press
DOI: 10.1016/j.jmaa.2016.05.045

Vector bundles for “Matrix algebras converge to the sphere”

Autori: Marc A. Rieffel
Pubblicato in: Journal of Geometry and Physics, Numero 132, 2018, Pagina/e 181-204, ISSN 0393-0440
Editore: Elsevier BV
DOI: 10.1016/j.geomphys.2018.06.003

The Podleś sphere as a spectral metric space

Autori: Konrad Aguilar, Jens Kaad
Pubblicato in: Journal of Geometry and Physics, Numero 133, 2018, Pagina/e 260-278, ISSN 0393-0440
Editore: Elsevier BV
DOI: 10.1016/j.geomphys.2018.07.015

Convergence of Cauchy sequences for the covariant Gromov–Hausdorff propinquity

Autori: Frédéric Latrémolière
Pubblicato in: Journal of Mathematical Analysis and Applications, Numero 469/1, 2019, Pagina/e 378-404, ISSN 0022-247X
Editore: Academic Press
DOI: 10.1016/j.jmaa.2018.09.018

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

Autori: Ludwik Dąbrowski, Francesco D’Andrea, Andrzej Sitarz
Pubblicato in: Letters in Mathematical Physics, Numero 108/5, 2018, Pagina/e 1323-1340, ISSN 0377-9017
Editore: Kluwer Academic Publishers
DOI: 10.1007/s11005-017-1036-x

Gauss-Bonnet for matrix conformally rescaled Dirac

Autori: Masoud Khalkhali, Andrzej Sitarz
Pubblicato in: Journal of Mathematical Physics, Numero 59/6, 2018, Pagina/e 063505, ISSN 0022-2488
Editore: American Institute of Physics
DOI: 10.1063/1.4997381

Spectral triples on the Jiang-Su algebra

Autori: Jacopo Bassi, Ludwik Dąbrowski
Pubblicato in: Journal of Mathematical Physics, Numero 59/5, 2018, Pagina/e 053507, ISSN 0022-2488
Editore: American Institute of Physics
DOI: 10.1063/1.5026311

Families of spectral triples and foliations of space(time)

Autori: Koen van den Dungen
Pubblicato in: Journal of Mathematical Physics, Numero 59/6, 2018, Pagina/e 063507, ISSN 0022-2488
Editore: American Institute of Physics
DOI: 10.1063/1.5021305

K-theory and index pairings for C*-algebras generated by $q$-normal operators

Autori: Ismael Cohen, Elmar Wagner
Pubblicato in: Rocky Mountain Journal of Mathematics, Numero 48/5, 2018, Pagina/e 1485-1510, ISSN 0035-7596
Editore: Rocky Mountain Mathematics Consortium
DOI: 10.1216/rmj-2018-48-5-1485

Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model

Autori: Ludwik Dąbrowski, Andrzej Sitarz
Pubblicato in: Journal of High Energy Physics, Numero 2019/2, 2019, ISSN 1029-8479
Editore: Institute of Physics Publishing
DOI: 10.1007/jhep02(2019)068

Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices

Autori: K. De Commer, M. Matassa
Pubblicato in: Advances in Mathematics, Numero 366, 2020, Pagina/e 107029, ISSN 0001-8708
Editore: Academic Press
DOI: 10.1016/j.aim.2020.107029

Triviality of equivariant maps in crossed products and matrix algebras

Autori: Benjamin W Passer
Pubblicato in: The Quarterly Journal of Mathematics, Numero 70/1, 2018, Pagina/e 289-303, ISSN 0033-5606
Editore: Oxford University Press
DOI: 10.1093/qmath/hay044

Representations of quantum SU(2) operators on a local chart

Autori: Elmar Wagner
Pubblicato in: Journal of Physics: Conference Series, Numero 670, 2016, Pagina/e 012053, ISSN 1742-6588
Editore: Institute of Physics
DOI: 10.1088/1742-6596/670/1/012053

Integrable lifts for transitive Lie algebroids

Autori: Iakovos Androulidakis, Paolo Antonini
Pubblicato in: International Journal of Mathematics, Numero 29/09, 2018, Pagina/e 1850062, ISSN 0129-167X
Editore: World Scientific Publishing Co
DOI: 10.1142/S0129167X18500623

Noncommutative Borsuk-Ulam-type conjectures

Autori: Paul F. Baum, Ludwik Dąbrowski, Piotr M. Hajac
Pubblicato in: Banach Center Publications, Numero 106, 2015, Pagina/e 9-18, ISSN 0137-6934
Editore: Banach Center Publications
DOI: 10.4064/bc106-0-1

Variations of projectivity for C∗-algebras

Autori: Don Hadwin, Tatiana Shulman
Pubblicato in: Pacific Journal of Mathematics, Numero 301/2, 2019, Pagina/e 421-440, ISSN 0030-8730
Editore: University of California at Berkeley
DOI: 10.2140/pjm.2019.301.421

The index of generalised Dirac–Schrödinger operators

Autori: Koen van den Dungen
Pubblicato in: Journal of Spectral Theory, Numero 9/4, 2019, Pagina/e 1459-1506, ISSN 1664-039X
Editore: European Mathematical Society Publishing House
DOI: 10.4171/JST/283

A Correspondence Between Homogeneous and Galois Coactions of Hopf Algebras

Autori: Kenny De Commer, Johan Konings
Pubblicato in: Algebras and Representation Theory, 2020, ISSN 1386-923X
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10468-019-09892-6

The modular Gromov–Hausdorff propinquity

Autori: Frédéric Latrémolière
Pubblicato in: Dissertationes Mathematicae, Numero 544, 2019, Pagina/e 1-70, ISSN 0012-3862
Editore: Institute of Mathematics, Polish Academy of Sciences
DOI: 10.4064/dm778-5-2019

The covariant Gromov–Hausdorff propinquity

Autori: Frédéric Latrémolière
Pubblicato in: Studia Mathematica, Numero 251/2, 2020, Pagina/e 135-169, ISSN 0039-3223
Editore: Polska Akademia Nauk
DOI: 10.4064/sm180610-28-12

Monic representations of finite higher-rank graphs

Autori: CARLA FARSI, ELIZABETH GILLASPY, PALLE JORGENSEN, SOORAN KANG, JUDITH PACKER
Pubblicato in: Ergodic Theory and Dynamical Systems, Numero 40/5, 2020, Pagina/e 1238-1267, ISSN 0143-3857
Editore: Cambridge University Press
DOI: 10.1017/etds.2018.79

Actions of categories by Lipschitz morphisms on limits for the Gromov–Hausdorff propinquity

Autori: Frédéric Latrémolière
Pubblicato in: Journal of Geometry and Physics, Numero 146, 2019, Pagina/e 103481, ISSN 0393-0440
Editore: Elsevier BV
DOI: 10.1016/j.geomphys.2019.103481

Spin geometry of the rational noncommutative torus

Autori: Alessandro Carotenuto, Ludwik Dąbrowski
Pubblicato in: Journal of Geometry and Physics, Numero 144, 2019, Pagina/e 28-42, ISSN 0393-0440
Editore: Elsevier BV
DOI: 10.1016/j.geomphys.2019.05.008

Model theory and Rokhlin dimension for compact quantum group actions

Autori: Eusebio Gardella, Mehrdad Kalantar, Martino Lupini
Pubblicato in: Journal of Noncommutative Geometry, Numero 13/2, 2019, Pagina/e 711-767, ISSN 1661-6952
Editore: European Mathematical Society Publishing House
DOI: 10.4171/jncg/337

Compact group actions on topological and noncommutative joins

Autori: Alexandru Chirvasitu, Benjamin Passer
Pubblicato in: Proceedings of the American Mathematical Society, Numero 146/8, 2018, Pagina/e 3217-3232, ISSN 0002-9939
Editore: American Mathematical Society
DOI: 10.1090/proc/13941

Dirac operator and its cohomology for the quantum group Uq()

Autori: Pavle Pandžić, Petr Somberg
Pubblicato in: Journal of Mathematical Physics, Numero 58/4, 2017, Pagina/e 041702, ISSN 0022-2488
Editore: American Institute of Physics
DOI: 10.1063/1.4979623

Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals

Autori: Konrad Aguilar
Pubblicato in: Journal of Operator Theory, 2019, ISSN 0379-4024
Editore: Academia Romana
DOI: 10.7900/jot.2018jun13.2222

Cuntz Semigroups of Compact-Type Hopf C*-Algebras

Autori: Dan Kučerovský
Pubblicato in: Axioms, Numero 6/4, 2017, Pagina/e 1, ISSN 2075-1680
Editore: MDPI
DOI: 10.3390/axioms6010001

Cotangent bundles for “matrix algebras converge to the sphere”

Autori: Marc A. Rieffel
Pubblicato in: Expositiones Mathematicae, 2020, ISSN 0723-0869
Editore: Elsevier BV
DOI: 10.1016/j.exmath.2020.01.006

Filtered K-theory for graph algebras

Autori: Søren Eilers, Gunnar Restorff, Efren Ruiz, Adam P.W. Sørensen
Pubblicato in: MATRIX Book Series, Numero 1, 2018, Pagina/e 229–249
Editore: Springer

On Noncommutative Geometry of the Standard Model: Fermion Multiplet as Internal Forms

Autori: Ludwik Dąbrowski
Pubblicato in: Geometric Methods in Physics XXXVI, 2017
Editore: Birkhäuser

Dirac Operator on a Noncommutative Toeplitz Torus

Autori: Fredy Díaz García, Elmar Wagner
Pubblicato in: Geometric Methods in Physics XXXVI - Workshop and Summer School, Białowieża, Poland, 2017, 2019, Pagina/e 103-109, ISBN 978-3-030-01155-0
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-01156-7_11

Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces

Autori: Francesca Arici, Piotr M. Hajac, Mariusz Tobolski
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

Standard homogeneous C*-algebras as compact quantum metric spaces

Autori: Konrad Aguilar, Tristan Bice
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

Some applications of conditional expectations to convergence for the quantum Gromov-Hausdorff propinquity

Autori: Konrad Aguilar, Frederic Latremoliere
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

Translations in quantum groups

Autori: Alexandru Chirvasitu
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

From Hopf algebras to topological quantum groups. A short history, various aspects and some problems

Autori: Alfons Van Daele
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

A spectral triple for noncommutative compact surfaces

Autori: Fredy Díaz García, Elmar Wagner
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

A note on the injectivity of action by compact quantum groups on a class of C∗-algebras

Autori: D Goswami, S Joardar
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

A graded pullback structure of Leavitt path algebras of trimmable graphs

Autori: Piotr M. Hajac, Atabey Kaygun, Mariusz Tobolski
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

Pullbacks of graph C*-algebras from admissible pushouts of graphs

Autori: Piotr M. Hajac, Sarah Reznikoff, Mariusz Tobolski
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

The asymptotic Connes-Moscovici characteristic map and the index cocycles

Autori: Atabey Kaygun, Serkan Sütlü
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

K-theory of cluster C*-algebras

Autori: Igor Nikolaev
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

Epsilon factors as algebraic characters on the smooth dual of GLn

Autori: Roger Plymen
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

A Note on the Quantum Family of Maps

Autori: Albert Jeu-Liang Sheu, Thomas Timmermann
Pubblicato in: Quantum Dynamics, 2020
Editore: Banach Center Publications

Equivariant Dimensions of Graph C*-algebras

Autori: Alexandru Chirvasitu, Benjamin Passer, Mariusz Tobolski
Pubblicato in: The Journal of Functional Analysis, 2020, ISSN 0022-1236
Editore: Academic Press

Invariant quantum measure on q-deformed twisted adjoint orbits

Autori: Kenny De Commer
Pubblicato in: Representation Theory, 2020, ISSN 1088-4165
Editore: American Mathematical Society

Twisted Dirac operator on quantum SU(2) in disc coordinates

Autori: Ulrich Kraehmer, Elmar Wagner
Pubblicato in: Operator Theory: Advances and Applications, 2020, ISSN 2543-0483
Editore: Springer Nature

Vector Bundles over Multipullback Quantum Complex Projective Spaces

Autori: Albert Jeu-Liang Sheu
Pubblicato in: Journal of Noncommutative Geometry, 2020, ISSN 1661-6952
Editore: European Mathematical Society Publishing House

Global symbolic calculus of pseudo-differential operators on homogeneous vector bundles

Autori: Mitsuru Wilson
Pubblicato in: SIGMA, 2020, ISSN 1815-0659
Editore: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine

The classification of Rokhlin flows on C*-algebras

Autori: Gabor Szabo
Pubblicato in: Communications in Mathematical Physics, 2020, ISSN 1432-0916
Editore: Springer

Noncommutative Borsuk-Ulam-type conjectures revisited

Autori: Ludwik Dąbrowski, Piotr M. Hajac, Sergey Neshveyev
Pubblicato in: JOURNAL OF NONCOMMUTATIVE GEOMETRY, 2020, ISSN 1661-6960
Editore: EMS
DOI: 10.4171/jncg/xxx

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