Simplicity of Pimsner algebras with application to quantum symmetries

Kan Kitamura (iTHEMS)

Thursday 9th October 16:00-17:00
Maths 116

Abstract

The Pimsner construction provides a convenient method for producing purely infinite simple C*-algebras. In this talk, we give a characterization of the simplicity of Pimsner algebras for non-proper C*-correspondences. With the aid of this simplicity criterion, we present a systematic strategy for constructing inclusions of Kirchberg algebras. In subfactor theory, it has been observed that inclusions of operator algebras often involve symmetries beyond groups, which can be formulated by actions of tensor categories. In the C*-algebraic setting, however, despite the rich variety of simple nuclear C*-algebras, relatively few examples of their inclusions were known. Our main motivation is to ensure the abundant existence of such inclusions in the purely infinite case.

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