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Noncommutative Analysis

A new universal AF-algebra

אפר 11, 11:00—12:00, 2022, 32/114

מרצה

Wieslaw Kubis (Institute of Mathematics, Prague)

תקציר

We introduce and study a new class of separable approximately finite-dimensional (AF) C* -algebras, namely, AF-algebras with ”Cantor property“. We show the existence of a separable AF-algebra A that is universal in the sense of quotients, i.e. every separable AF-algebra is a quotient of A. Moreover, a natural extension property involving left-invertible embeddings describes it uniquely up to isomorphism.

This is a joint work with Saeed Ghasemi. The paper is Universal AF-algebras. J. Funct. Anal. 279 (2020), no. 5, 108590, 32 pp.

קולוקוויום

Relations between dynamics and C*-algebras: Mean dimension and radius of comparison

אפר 12, 14:30—15:30, 2022, Math -101

מרצה

Chris Phillips (University of Oregon)

תקציר

This is joint work with Ilan Hirshberg.

For an action of an amenable group G on a compact metric space X, the mean dimension mdim (G, X) was introduced by Lindenstrauss and Weiss. It is designed so that the mean dimension of the shift on ([0, 1]^d)^G is d. Its motivation was unrelated to C*-algebras.

The radius of comparison rc (A) of a C*-algebra A was introduced by Toms to distinguish counterexamples in the Elliott classification program. The algebras he used have nothing to do with dynamics.

A construction called the crossed product C^* (G, X) associates a C-algebra to a dynamical system. Despite the apparent lack of connection between these concepts, there is significant evidence for the conjecture that rc ( C^ (G, X) ) = (1/2) mdim (G, X) when the action is free and minimal. We will explain the concepts above; no previous knowledge of mean dimension, C-algebras, or radius of comparison will be assumed. Then we describe some of the evidence. In particular, we give the first general partial results towards the direction rc ( C^ (G, X) ) \geq (1/2) mdim (G, X). We don‘t get the exact conjectured bound, but we get nontrivial results for many of the known examples of free minimal systems with mdim (G, X) > 0.

AGNT

תב“ה

אפר 13, 16:00—17:15, 2022, -101

מרצה

No meeting

BGU Probability and Ergodic Theory (PET) seminar

Passover break

אפר 14, 11:10—12:00, 2022, -101

מרצה

Holiday


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