Lie groups as permutation groups: Ulam's problem in the nilpotent case

DOI10.1515/JGTH-2021-0168arXiv2110.01650MaRDI QIDQ6379357

Publication date: 4 October 2021

Abstract: Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate the relevance of nilpotent groups for Ulam's problem.

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Nilpotent and solvable Lie groups (22E25) General theory for infinite permutation groups (20B07)

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