Journal of Lie Theory 31 (2021), No. 4, 1071--1084
Copyright Heldermann Verlag 2021
The Hilbert's Fifth Problem for Totally Intransitive Groupoids
Pawel Razny
Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
pawel.razny@uj.edu.pl
We continue the study of the Hilbert's fifth problem for groupoids by giving results concerning the totally intransitive case. We start by constructing a counterexample to the problem in its most general form. We then continue by noting the key feature of this example to give a positive answer to the problem under the additional assumptions that among the Lie algebras of the automorphism groups there is at most a finite collection of pairwise non-isomorphic Lie algebras and the base is of dimension 1. On the way we reduce the problem (for arbitrary dimension of the base) to smoothing a continuous Lie algebra bundle derived from the groupoid.
Keywords: Lie groupoids, topological groupoids.
MSC: 22A22.
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