Geodesic
On Epimorphisms in some Categories of Infinite-Dimensional Lie Groups
Vladimir G. Pestov1, 2 ; Vladimir V. Uspenskij3
1Dep. de Matemática, Universidade Federal de Santa Catarina, Trindade, Florianópolis, Brazil
2Dept of Mathematics and Statistics, University of Ottawa, Ontario, Canada
3Dept. of Mathematics, Ohio University, Athens, Ohio 45701, U.S.A.
Journal of Lie Theory, Tome 31 (2021) no. 3, pp. 871-884

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

Let $X$ be a smooth compact connected manifold. Let $G=\text{Diff}\,X$ be the group of diffeomorphisms of $X$, equipped with the $C^\infty$-topology, and let $H$ be the stabilizer of some point in $X$. Then the inclusion $H\to G$, which is a morphism of two regular Fr\'echet-Lie groups, is an epimorphism in the category of smooth Lie groups modelled on complete locally convex spaces. At the same time, in the latter category, epimorphisms between finite dimensional Lie groups have dense range. We also prove that if $G$ is a Banach-Lie group and $H$ is a proper closed subgroup, the inclusion $H\to G$ is not an epimorphism in the category of Hausdorff topological groups.
Classification : 18A20, 22E65, 58D05
Mots-clés : Epimorphism, locally convex Lie group, Frechet-Lie group, Banach-Lie group, Hausdorff topological group

Vladimir G. Pestov  1 , 2   ; Vladimir V. Uspenskij  3

1 Dep. de Matemática, Universidade Federal de Santa Catarina, Trindade, Florianópolis, Brazil
2 Dept of Mathematics and Statistics, University of Ottawa, Ontario, Canada
3 Dept. of Mathematics, Ohio University, Athens, Ohio 45701, U.S.A. 
Vladimir G. Pestov; Vladimir V. Uspenskij. On Epimorphisms in some Categories of Infinite-Dimensional Lie Groups. Journal of Lie Theory, Tome 31 (2021) no. 3, pp. 871-884. http://geodesic.mathdoc.fr/item/JOLT_2021_31_3_a10/
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     title = {On {Epimorphisms} in some {Categories} of {Infinite-Dimensional} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {871--884},
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