Strong Morita equivalence for inclusions of C^*-algebras induced by twisted actions of a countable discrete group

2019/10/08 by Kazunori Kodaka, Kodaka, Kazunori
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #math.OA #msc:46L05

paper · pdf · doi:10.48550/arxiv.1910.03774

14 pages. This is a third version of arXiv:1910.03774

arxiv created 2020/11/13 · arxiv updated 2020/11/16

Abstract

We consider two twisted actions of a countable discrete group on σ-unital C^*-algebras. Then by taking the reduced crossed products, we get two inclusions of C^*-algebras. We suppose that they are strongly Morita equivalent as inclusions of C^*-algebras. Also, we suppose that one of the inclusions is irreducible, that is, the relative commutant of one of the σ-unital C^*-algebra in the multiplier C^*-algebra of the reduced twisted crossed product is trivial. We show that the two actions are then strongly Morita equivalent up to some automorphism of the group.

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