Equivariant semiprojectivity

2011/12/20 by N. Christopher Phillips, Phillips, N. Christopher · 1 citation
Mathematics · Physics and Astronomy · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.1112.4584

44 pages; AMSLaTeX

arxiv created 2011/12/20 · openalex publication_date 2011/12/20 · arxiv updated 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define equivariant semiprojectivity for C*-algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: arbitrary finite dimensional C*-algebras with arbitrary actions of compact groups; the Cuntz algebras O_d and extended Cuntz algebras E_d, for finite d, with quasifree actions of compact groups; the Cuntz algebra O_∞ with any quasifree action of a finite group. For actions of finite groups, we prove that equivariant semiprojectivity is equivalent to a form of equivariant stability of generators and relations. We also prove that if G is finite, then C^* (G) is graded semiprojective.

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