Geodesic
The Hilbert's Fifth Problem for Totally Intransitive Groupoids
Pawel Razny1
1Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1071-1084

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22A22
Mots-clés : Lie groupoids, topological groupoids

Pawel Razny  1

1 Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland 
Pawel Razny. The Hilbert's Fifth Problem for Totally Intransitive Groupoids. Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1071-1084. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a12/
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     title = {The {Hilbert's} {Fifth} {Problem} for {Totally} {Intransitive} {Groupoids}},
     journal = {Journal of Lie Theory},
     pages = {1071--1084},
     year = {2021},
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