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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.04408 |
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| _version_ | 1866914779752300544 |
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| author | Caprace, P. -E. Minasyan, A. Osin, D. |
| author_facet | Caprace, P. -E. Minasyan, A. Osin, D. |
| contents | For each prime $p$ and each positive integer $d$, we construct the first examples of second countable, topologically simple, $p$-adic Lie groups of dimension $d$ whose Lie algebras are abelian. This answers several questions of Glöckner and Caprace-Monod. The proof relies on a generalization of small cancellation methods that applies to central extensions of acylindrically hyperbolic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04408 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simple $p$-adic Lie groups with abelian Lie algebras Caprace, P. -E. Minasyan, A. Osin, D. Group Theory For each prime $p$ and each positive integer $d$, we construct the first examples of second countable, topologically simple, $p$-adic Lie groups of dimension $d$ whose Lie algebras are abelian. This answers several questions of Glöckner and Caprace-Monod. The proof relies on a generalization of small cancellation methods that applies to central extensions of acylindrically hyperbolic groups. |
| title | Simple $p$-adic Lie groups with abelian Lie algebras |
| topic | Group Theory |
| url | https://arxiv.org/abs/2308.04408 |