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arXiv · 2310.11922

An application of Kirchberg's lemma on central sequence algebras to groups of approximately inner automorphisms

Hiroshi Ando·Michal Doucha
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Abstract

We revisit a well-known "surjectivity onto quotient" type lemma of Kirchberg on the central sequence algebra of a separable unital ${\rm C}^*$-algebra, and use it to prove a "surjectivity onto quotient" result on approximately inner automorphisms of a separable unital ${\rm C}^*$-algebra of stable rank one, which we can partially upgrade also to the non-separable case.

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Hiroshi Ando, Michal Doucha. 2023-10-18. An application of Kirchberg's lemma on central sequence algebras to groups of approximately inner automorphisms. https://arxiv.org/abs/2310.11922

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