A note on trace scaling actions and fundamental groups of C^*-algebras

2010/09/09 by Norio Nawata, Nawata, Norio
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L40 #Secondary 06F20

paper · pdf · doi:10.48550/arxiv.1009.1722

openalex publication_date 2010/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Effros-Handelman-Shen theorem and Elliott's classification theorem of AF algebras, we show that there exists a unital simple AF algebra A with unique trace such that A⊗ \mathbbK admits no trace scaling action of the fundamental group of A.

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• Fundamental group of simple C^*-algebras with unique trace III
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• Subalgebras of simple AF-algebras