Lie groups in the symmetric group: Reducing Ulam's problem to the simple case
2023
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.
Details
Title
Lie groups in the symmetric group: Reducing Ulam's problem to the simple case
Author(s)
Conversano, Annalisa ; Monod, Nicolas
Published in
Journal Of Algebra
Volume
640
Pages
106-116
Date
2023-11-21
Publisher
Academic Press Inc Elsevier Science, San Diego
ISSN
0021-8693
1090-266X
1090-266X
Keywords
Other identifier(s)
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Laboratories
EGG
Record Appears in
Scientific production and competences > SB - School of Basic Sciences > MATH - Institute of Mathematics > EGG - Chair of ergodic and geometric group theory
Scientific production and competences > SB - School of Basic Sciences > Mathematics
Peer-reviewed publications
Work produced at EPFL
Journal Articles
Published
Scientific production and competences > SB - School of Basic Sciences > Mathematics
Peer-reviewed publications
Work produced at EPFL
Journal Articles
Published
Record creation date
2024-02-20