H2020Индивидуална стипендия2018–2019

SCCD · Structure and classification of C*-dynamics

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2018-01-01 → 2019-12-31
Финансиране от ЕС: 200 195 €
Участници: 1
Схема: MSCA-IF

Линиите свързват координатора с партньорите.

Накратко на български

C-алгебрите и тяхната динамика изследват математическите структури на некомутативните пространства, като например описанието на времето в една физична система. Тези проучвания помагат за класифицирането на обобщени симетрии и разбирането на сложни динамични процеси.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Structure and classification of C*-dynamics

The research outcome concerns the structure theory of C*-algebras, which is a branch of functional analysis. The focus lies on noncommutative dynamical systems, or also called C*-dynamics, which can for example be a mathematical description of a time evolution in a physical system. Of particular interest are dynamical structures on simple nuclear C*-algebras, which can be thought of as noncommutative topological spaces that are indecomposable into smaller pieces. The classification theory for the underlying objects has made big steps in recent years, and the research carried out over this project capitalizes on the new techniques to study dynamics on them, which can be thought of as generalized symmetries. The main objectives can be summarized as follows: 1) To test a potential classification theory for actions of amenable groups on the class of strongly self-absorbing C*-algebras, which are particularly rigid in nature. 2) Investigate the fine structure group actions on purely infinite C*-algebras, which can be thought of as the well-understood low-dimensional noncommutative spaces. 3) Classify time evolutions, or flows, on classifiable classes of C*-algebras. Of particular interest are flows with the so-called Rokhlin property a la Kishimoto.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

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.

Оригинален текст от CORDIS (на английски).

Участници

KOBENHAVNS UNIVERSITET · KOBENHAVNКоординаторДания