Publication

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Nicolas Monod
2023
Journal Articles

Abstract

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups with a linear Levi component. It follows that every amenable locally compact second countable group acts faithfully on a countable set.(c) 2023 Elsevier Inc. All rights reserved.

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Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

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