Coronas and strongly self-absorbing C*-algebras

Gabor Szabo (KU Leuven)

Thursday 6th February 16:00-17:00 Maths 311B

Abstract

The corona algebra of a non-unital C*-algebra A is defined as the quotient of the multiplier algebra modulo A itself. The corona is the noncommutative analog of the Stone-Cech boundary of a space and is particularly interesting when A is stable. These objects naturally appear in Ext-theory or KK-theory, where more detailed structural behavior is at times relevant for classification. A few years ago, Farah published an article in which he proved that the Calkin algebra is not isomorphic to the stable corona of any infinite-dimensional unital classifiable C*-algebra. Prior to that, it has been open for some time whether the Calkin algebra is isomorphic to the stable corona of the Cuntz algebra of infinitely many generators, which was tied to some other open questions about the structure of the Calkin algebra. Farah's proof of this non-isomorphism involved several interesting overarching observations about the structure of stable coronas of C*-algebras that tensorially absorb any given strongly self-absorbing C*-algebra D. In this talk I want to report on a continuation of Farah's work, obtained in joint work with Farah: For every sigma-unital C*-algebra A, one has that A is separably D-stable if and only if the stable corona of A is separably D-stable. If time permits, I will discuss some non-trivial applications of this result.

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