Lie groups as permutation groups: Ulam's problem in the nilpotent case
Group Theory
2021-10-11 v3 Representation Theory
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.
Keywords
Cite
@article{arxiv.2110.01650,
title = {Lie groups as permutation groups: Ulam's problem in the nilpotent case},
author = {Nicolas Monod},
journal= {arXiv preprint arXiv:2110.01650},
year = {2021}
}
Comments
v2: correction in last section and added references; v3: extended Thm. 6