Interactions between von Neumann algebras and quantum algebras

Informazioni relative al progetto

INNEQUAL

ID dell’accordo di sovvenzione: 702139

DOI

10.3030/702139

Progetto concluso il 1 Settembre 2017

Data della firma CE 22 Febbraio 2016

Data di avvio 1 Settembre 2016

Data di completamento 31 Agosto 2018

Finanziato da

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Costo totale

€ 165 598,80

Contributo UE

€ 165 598,80

Coordinato da

UNIVERSITEIT UTRECHT
Netherlands

Periodic Reporting for period 1 - INNEQUAL (Interactions between von Neumann algebras and quantum algebras)

Periodo di rendicontazione: 2016-09-01 al 2018-08-31

Sintesi del contesto e degli obiettivi generali del progetto

What is the problem/issue being addressed?

The project deals with the structural of q-deformed von Neumann algebras. These are mathematical frameworks to model quantum observables, originally introduced by von Neumann and having several applications in quantum theory and branches of pure mathematics. The project focusses on classification, where in recent years breakthrough results have been obtained for group von Neumann algebras. The proposal brings this classification programme forward by starting the investigation of q-deformed algebras or quantum algebras. Such algebras emerge in quantum gravity and by its formalism generate new classes of von Neumann algebras which in view of this classification programme not much is known.

Why is it important for society?

There is no direct relevance for society, the project deals with pure mathematics.

What are the overall objectives?

1) Obtain classification results for von Neumann algebras
2) Construct new von Neumann algebras of the rare class of `Type III' algebras
3) Applications to geometry and geometric group theory

Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti

Research output in the period September 2016-August 2017:

2 preprints:
-1 on structural properties of q-deformations (submitted).
-1 on perturbations of commutators (accepted for Annales de l'Institut Fourier).

1 preprint in preparation:
-1 on strong solidity of free quantum groups (submitted in February 2019)

Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora)

I found new estimates for commutators extending earlier work by myself, coauthors and others. I also found very interesting properties of MASAs in q-Gaussian algebras and obstructions to mutual embeddability for them.

No more results are expected as the project is terminated. I found a permanent (tenure track) job shortly after the project started and therefore had to terminate the grant agreement after 1 year (so when the new job actually started). After continuing research new results have been obtained that address especially the Objectives 1 and 3 mentioned above.

Impact lies in general operator theory and noncommutative analysis. A wider societal impact is not expected.

EU Logo