Regular inclusions of simple unital C^*-algebras

2024/04/10 by Bakshi, Keshab Chandra, Gupta, Ved Prakash · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2404.06959

Abstract

We prove that an inclusion B ⊂ A of simple unital C^*-algebras with a finite-index conditional expectation is regular if and only if there exists a finite group G that admits a cocycle action (α,σ) on the intermediate C^*-subalgebra C generated by B and its centralizer C_A(B) such that B is outerly α-invariant and (B ⊂ A) ≅ ( B ⊂ C\rtimes^r_{α, σ} G). Prior to this characterization, we prove the existence of two-sided and unitary quasi-bases for the minimal conditional expectation of any such inclusion, and also show that such an inclusion has integer Watatani index and depth at most 2.

Cited by

• Depth 2 inclusions of simple C^*-algebras and their weak C^*-Hopf algebra symmetries

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• Inclusions of simple C^*-algebras
• Structure for Regular Inclusions
• Inclusions of C^*-algebras arising from fixed-point algebras
• Cancellation for inclusions of C*-algebras of finite depth
• Unique conditional expectations for abelian C^*-inclusions