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

2010/06/29 by Norio Nawata, Nawata, Norio
Mathematics · Physics and Astronomy · #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Primary 46L05 #Secondary 46L08

paper · pdf · doi:10.48550/arxiv.1006.5501

openalex publication_date 2010/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the fundamental group F(A) of a simple σ-unital C^*-algebra A with unique (up to scalar multiple) densely defined lower semicontinuous trace. This is a generalization of our previous works. Our definition in this paper makes sense for stably projectionless C^*-algebras. We show that there exist separable stably projectionless C^*-algebras such that their fundamental groups are equal to ℝ₊^× by using the classification theorem of Razak and Tsang. This is a contrast to the unital case. This study is motivated by the work of Kishimoto and Kumjian.

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