New tensor products of C*-algebras and characterization of type I C*-algebras as rigidly symmetric C*-algebras

Abstract: C*-algebras are studied through various tools and techniques including their tensor products. There are several classes of tensor products that have been considered and studied extensively on C*-algebras. We introduce a new class of such objects using the theory of complex interpolations on operator spaces. Our construction allows us to produce a continuum family of distinct tensor product of the reduced C*-algebras of nonamenable groups possessing both the rapid decay and Haagerup property. We will show that they are in fact in the form of a Brown-Guentner type C*-completion. As another application of our approach, we provide a complete answer to a question of Leptin and Poguntke from 1979 proving that a C*-algebra is rigidly symmetric if and only if it is type I.

This talk is based on a joint work with Hun Hee Lee (SNU) and Matthew Wiersma (U of Winnipeg).

functional analysisoperator algebras

Audience: researchers in the discipline

Functional analysis and operator algebras in Athens

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