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

2023/10/18 by Hiroshi Ando, Michal Doucha, Ando, Hiroshi +1
Mathematics · #46L05 #46M07 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2310.11922

openalex publication_date 2023/10/18 · openalex created_date 2023/10/21 · openalex updated_date 2026/07/28

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.

Related

• Centrally pure C*-algebras
• A dichotomy for central sequence algebras
• Commutativity of central sequence algebras
• The Ext class of an approximately inner automorphism, II
• Central Sequences in Subhomogeneous Unital C*-algebras