On the smoothness of some quotients of Banach-Lie groups |
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Institution: | 1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania;2. Unité Mixte de Recherche 5127 CNRS, Université Savoie Mont Blanc, Laboratoire de Mathématiques (LAMA), Chambéry, France;3. University of Sousse, Higher Institute of Applied Sciences and Technology of Sousse, Mathematical Physics Laboratory, Special Functions and Applications, City Ibn Khaldoun 4003, Sousse, Tunisia |
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Abstract: | Quotients of Banach-Lie groups are regarded as topological groups with Lie algebra in the sense of Hofmann-Morris on the one hand, and as Q-groups in the sense of Barre-Plaisant on the other hand. For the groups of the type where is a pseudo-discrete normal subgroup, their Lie algebra in the sense of Q-groups turns out to be isomorphic to the Lie algebra of G, which is in general merely a dense subalgebra of the Lie algebra of when regarded as a topological group with Lie algebra. The submersion-like behavior of quotient maps of Banach-Lie groups is also investigated. The two aforementioned approaches to the Lie theory of the quotients of Banach-Lie groups thus lead to differing results and the Lie theoretic properties of quotient groups are more accurately described by the Q-group approach than by the approach via topological groups with Lie algebras. |
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Keywords: | Banach-Lie group Topological group with Lie algebra Q-manifold |
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