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

Author:

Monod Nicolas1

Affiliation:

1. EPFL , Lausanne , Switzerland

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference34 articles.

1. G. Birkhoff, Lie groups simply isomorphic with no linear group, Bull. Amer. Math. Soc. 42 (1936), no. 12, 883–888.

2. K. S. Brown, Cohomology of Goups, Grad. Texts in Math. 87, Springer, New York, 1982.

3. É. Cartan, La topologie des groupes de Lie. (Exposés de géométrie VIII), Actual. Sci. Indus. 358 (1936), 1–28.

4. V. A. Churkin, Examples of groups with continuum cardinality that are not embeddable into the permutation group of a countable set, Algebra and Model Theory 5, Novosibirsk State Technical University, Novosibirsk (2005), 39–43.

5. W. W. Comfort, Topological groups, Handbook of Set-Theoretic Topology, North-Holland, Amsterdam (1984), 1143–1263.

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