Some remarks on decay in countable groups and amalgamated free products
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909780393590784 |
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| author | Elayavalli, Srivatsav Kunnawalkam Patchell, Gregory Teryoshin, Lizzy |
| author_facet | Elayavalli, Srivatsav Kunnawalkam Patchell, Gregory Teryoshin, Lizzy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some remarks on decay in countable groups and amalgamated free products Elayavalli, Srivatsav Kunnawalkam Patchell, Gregory Teryoshin, Lizzy Group Theory Functional Analysis Operator Algebras 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. |
| title | Some remarks on decay in countable groups and amalgamated free products |
| topic | Group Theory Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2509.08754 |