Journal of Lie Theory

no. 4
The Hilbert's Fifth Problem for Totally Intransitive Groupoids
Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1071-1084
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.
DOI: 10.5802/jolt.1212
Classification: 22A22
Keywords: Lie groupoids, topological groupoids 
@article{JOLT_2021_31_4_a12,
     author = {P. Razny},
     title = {The {Hilbert's} {Fifth} {Problem} for {Totally} {Intransitive} {Groupoids}},
     journal = {Journal of Lie Theory},
     pages = {1071--1084},
     year = {2021},
     volume = {31},
     number = {4},
     doi = {10.5802/jolt.1212},
     zbl = {1486.22003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1212/}
}
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P. Razny. The Hilbert's Fifth Problem for Totally Intransitive Groupoids. Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 1071-1084. doi: 10.5802/jolt.1212

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