Topological stable rank of inclusions of unital C*-algebras

2003/11/26 by Hiroyuki Osaka, Osaka, Hiroyuki, Tamotsu Teruya +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.math/0311461

Abstract

Let 1 ∈ A ⊂ B be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of B (= \tsr(B)) when A has topological stable rank one. We show that \tsr(B) ≤ 2 when A is a tsr boundedly divisible algebra, in particular, A is a C*-minimal tensor product UHF ⊗ D with \tsr(D) = 1. When G is a finite group and α is an action of G on UHF, we know that a crossed product algebra UHF \rtimes_αG has topological stable rank less than or equal to two. These results are affirmative datum to a generalization of a question by B. Blackadar in 1988.

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• Periodic cyclic homology of affine Hecke algebras

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