Simple p-adic Lie groups with abelian Lie algebras

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

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