Simple 𝑝-adic Lie groups with abelian Lie algebras
-
Pierre-Emmanuel Caprace
and
Denis 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 Glöckner and Caprace–Monod. The proof relies on a generalization of small cancellation methods that applies to central extensions of acylindrically hyperbolic groups.
Funding source: Fonds Wetenschappelijk Onderzoek
Award Identifier / Grant number: 40007542
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1853989
Funding statement: P.-E. Caprace has been supported in part by the FWO and the F.R.S.-FNRS under the EOS programme (project ID 40007542). D. Osin has been supported by the NSF grant DMS-1853989.
Acknowledgements
The authors would like to thank the anonymous referee for carefully reading a draft of this paper, and for a number of suggestions that improved the exposition.
References
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Articles in the same Issue
- Frontmatter
- The theory of F-rational signature
- Jacobian determinants for nonlinear gradient of planar ∞-harmonic functions and applications
- Fano varieties with torsion in the third cohomology group
- The distribution of Manin’s iterated integrals of modular forms
- On some 𝑝-adic and mod 𝑝 representations of quaternion algebra over ℚ𝑝
- Nonexistence of isoperimetric sets in spaces of positive curvature
- Simple 𝑝-adic Lie groups with abelian Lie algebras
- Hyperbolic lattice point counting in unbounded rank
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Articles in the same Issue
- Frontmatter
- The theory of F-rational signature
- Jacobian determinants for nonlinear gradient of planar ∞-harmonic functions and applications
- Fano varieties with torsion in the third cohomology group
- The distribution of Manin’s iterated integrals of modular forms
- On some 𝑝-adic and mod 𝑝 representations of quaternion algebra over ℚ𝑝
- Nonexistence of isoperimetric sets in spaces of positive curvature
- Simple 𝑝-adic Lie groups with abelian Lie algebras
- Hyperbolic lattice point counting in unbounded rank
- The (almost) integral Chow ring of ℳ̅3
