The radius of comparison for actions of Z^d on simple AH algebras

Given 0 \leq r' \leq r \leq \infty, and d \in N, we construct a simple unital AH algebra A with stable rank one, and a pointwise outer action \alpha : Z^d \to Aut(A), such that rc(A)=r and rc (A \rtimes_{\alpha} Z^d)=r'.

Publication Details

Journal
ArXiv.org
Published
2025-03-07
Primary Topic
Advanced Operator Algebra Research
Type
article
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article

The radius of comparison for actions of Z^d on simple AH algebras

ArXiv.org
Advanced Operator Algebra Research
article

The radius of comparison for actions of Z^d on simple AH algebras

article en

Abstract

Given 0 \leq r' \leq r \leq \infty, and d \in N, we construct a simple unital AH algebra A with stable rank one, and a pointwise outer action \alpha : Z^d \to Aut(A), such that rc(A)=r and rc (A \rtimes_{\alpha} Z^d)=r'.

ArXiv.org
Openalex Percentile: Top 46%
Advanced Operator Algebra Research
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The radius of comparison for actions of Z^d on simple AH algebras · ArXiv.org (2025) | TGRS Research Map | TGRS