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Some remarks on decay in countable groups and amalgamated free products

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arxiv 2509.08754 v1 pith:WJZLLSLD submitted 2025-09-10 math.GR math.FAmath.OA

Srivatsav Kunnawalkam Elayavalli , Gregory Patchell , Lizzy Teryoshin This is my paper · ORCID
classification math.GRmath.FAmath.OA
keywords decaygroupsamalgamatedcountablefirstfreeproductsalgebras
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abstract

In this note, we first study the notion of subexponential decay (SD) for countable groups with respect to a length function, which generalizes the well-known rapid decay (RD) property, first discovered by Haagerup in 1979. Several natural properties and examples are studied, especially including groups that have SD, but not RD. This consideration naturally has applications in $C^*$-algebras. We also consider in this setting a permanence theorem for decay in amalgamated free products (proved also recently by Chatterji--Gautero), and demonstrate that it is in a precise sense optimal.

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Cited by 4 Pith papers

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