Structure and classification of C*-dynamics

Información del proyecto

SCCD

Identificador del acuerdo de subvención: 746272

DOI

10.3030/746272

Proyecto finalizado el 30 Septiembre 2018

Fecha de la firma de la CE 12 Diciembre 2017

Fecha de inicio 1 Enero 2018

Fecha de finalización 31 Diciembre 2019

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 200 194,80

Aportación de la UE

€ 200 194,80

Coordinado por

KOBENHAVNS UNIVERSITET
Denmark

Objetivo

We study group actions on C*-algebras from a structure and classification point of view, importing concepts from the Elliott classification program into the equivariant context. The challenge is to advance the structure theory for natural classes of actions of amenable groups on C*-algebras. In a similar vein, we shall consider flows on C*-algebras, which are the mathematical abstractions of time evolutions. The objectives of this proposal are:

A: Establish an Ocneanu-type rigidity result for actions of amenable groups on strongly self-absorbing C*-algebras as well as the automatic tensorial absorption of such actions under natural conditions.

B: Obtain an equivariant version of the KK-theoretic stable uniqueness theorem à la Lin-Dadarlat-Eilers.

C: Study the rigid behavior of flows on Kirchberg algebras with the Rokhlin property, in order to solve a long-standing open problem set out by Kishimoto. We also consider other natural classes of flows without the Rokhlin property, the projected classification of which will solve open problems such as Robert's conjecture and part of the Toms-Winter conjecture.

The solution to this challenge employs equivariant generalizations of important classical concepts like strong self-absorption, W*-bundles, KK-theory, and combines these with known concepts like Rokhlin dimension in an innovative way. The projected results are ground-breaking for the field of C*-algebras, and the methods to obtain them go well beyond the state-of-the-art. The projects are chosen to maximize the transfer of knowledge between the ER and the supervisor. Taking into account the excellent opportunities for professional training and public engagement provided by the University of Aberdeen as well as the other suggested activities described in the proposal, the MSC IF will have a substantial impact on the ER’s career, qualifying him for a permanent position at a research-driven institution after completing the fellowship.

Ámbito científico (EuroSciVoc)

• ciencias naturales › matemáticas › matemáticas aplicadas › sistemas dinámicos
• ciencias naturales › matemáticas › matemáticas puras › álgebra
• ciencias naturales › matemáticas › matemáticas puras › análisis matemático › análisis funcional › álgebra de operadores

Palabras clave

• C*-algebras
• group actions
• C*-dynamics
• flows
• one-parameter automorphisms

Programa(s)

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions PROGRAMA PRINCIPAL
  
• H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
  

Tema(s)

• MSCA-IF-2016 - Individual Fellowships
  

Régimen de financiación

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

Convocatoria de propuestas

H2020-MSCA-IF-2016

Coordinador

KOBENHAVNS UNIVERSITET

• Aportación neta de la UEn: € 200 194,80
• Dirección: NORREGADE 10 ; 1165 KOBENHAVN ; Dinamarca
• Región: Danmark › Hovedstaden › Byen København
• Tipo de actividad: Higher or Secondary Education Establishments
• Coste total: € 200 194,80