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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.07994 |
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| _version_ | 1866917423752413184 |
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| author | Chatterji, Indira Zarka, Benjamin |
| author_facet | Chatterji, Indira Zarka, Benjamin |
| contents | We generalize the notion of rapid decay property for a group $G$ to pairs of groups $(G,H)$ where $H$ is a finitely generated subgroup of $G$, where typically the subgroup $H$ does not have rapid decay. We deduce some isomorphisms in $K$-theory, and investigate relatively spectral injections in the reduced group $C^*$-algebra. Rapid decay property for the pair $(G,H)$ also gives a lower bound for the probability of return to $H$ of symmetric random walks on $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The rapid decay property for pairs of discrete groups Chatterji, Indira Zarka, Benjamin Operator Algebras Functional Analysis Group Theory K-Theory and Homology Probability 19, 20, 46, 47 We generalize the notion of rapid decay property for a group $G$ to pairs of groups $(G,H)$ where $H$ is a finitely generated subgroup of $G$, where typically the subgroup $H$ does not have rapid decay. We deduce some isomorphisms in $K$-theory, and investigate relatively spectral injections in the reduced group $C^*$-algebra. Rapid decay property for the pair $(G,H)$ also gives a lower bound for the probability of return to $H$ of symmetric random walks on $G$. |
| title | The rapid decay property for pairs of discrete groups |
| topic | Operator Algebras Functional Analysis Group Theory K-Theory and Homology Probability 19, 20, 46, 47 |
| url | https://arxiv.org/abs/2412.07994 |