Simple $p$-adic Lie groups with abelian Lie algebras

P. -E. Caprace; A. Minasyan; D. Osin

Simple $p$-adic Lie groups with abelian Lie algebras

Group Theory 2024-05-03 v3

Authors: P. -E. Caprace , A. Minasyan , D. Osin

Abstract

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 Gl\"ockner and Caprace-Monod. The proof relies on a generalization of small cancellation methods that applies to central extensions of acylindrically hyperbolic groups.

Keywords

lie algebra abelian groups finite groups

Cite

@article{arxiv.2308.04408,
  title  = {Simple $p$-adic Lie groups with abelian Lie algebras},
  author = {P. -E. Caprace and A. Minasyan and D. Osin},
  journal= {arXiv preprint arXiv:2308.04408},
  year   = {2024}
}

Comments

Minor corrections. To appear in Crelle

Simple $p$-adic Lie groups with abelian Lie algebras

Abstract

Keywords

Cite

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