The inverse-closed subalgebra of C^*(G,A)

2025/04/23 by Jianjun Chen, Chen, Jianjun
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2504.17495

openalex publication_date 2025/04/23 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

This paper studies the inverse-closed subalgebras of the Roe algebra with coefficients of the type \(l²(G, A)\). The coefficient \(A\) is chosen to be a non-commutative \(C^*\)-algebra, and the object of study is \(C^*(G, A)\) generated by the countable discrete group \(G\). By referring to the Sobolev-type algebra, the intersection of a family of Banach algebras is taken. It is proved that the intersection \(W_a^∞(G, A)\) of Banach spaces is a spectrally invariant dense subalgebra of \(C^*(G, A)\), and a sufficient condition for this is that the group action of \(G\) has polynomial growth.

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