The Ext class of an approximately inner automorphism, II

1998/05/20 by Akitaka Kishimoto, A. Kishimoto, Kishimoto, A. +3
Mathematics · #46L35 #46L40 #46L80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras #math.OA #msc:46L35 #msc:46L40 #msc:46L80

paper · pdf · doi:10.48550/arxiv.math/9805085

20 pages

arxiv created 1998/05/20 · openalex publication_date 1998/05/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a simple unital AT algebra of real rank zero and Inn(A) the group of inner automorphisms of A. In the previous paper we have shown that the natural map of the group of approximately inner automorphisms into Ext(K₁(A),K₀(A)) oplus Ext(K₀(A),K₁(A)) is surjective; the kernel of this map includes the subgroup of automorphisms which are homotopic to Inn(A). In this paper we consider the quotient of the group of approximately inner automorphisms by the smaller normal subgroup AInn(A) which consists of asymptotically inner automorphisms and describe it as OrderExt(K₁(A),K₀(A)) oplus Ext(K₀(A),K₁(A)), where OrderExt(K₁(A),K₀(A)) is a kind of extension group which takes into account the fact that K₀(A) is an ordered group and has the usual Ext as a quotient.

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