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arXiv · 2504.17495

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

Jianjun Chen
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Abstract

This paper studies the inverse-closed subalgebras of the Roe algebra with coefficients of the type \(l^2(G, A)\). 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 \(W_a^{\infty}(G, A)\) 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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Jianjun Chen. 2025-04-23. The inverse-closed subalgebra of $C^{*}(G,A)$. https://arxiv.org/abs/2504.17495

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