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The Existence of Coupling in the Category of Transitive Lie Algebroidстатья
- Авторы: Xiaoyu Li, Mishchenko Alexander S.
- Журнал: Electronic archive:arXiv:1306.5449
- Год издания: 2013
- Первая страница: 1
- Последняя страница: 8
- Аннотация: The coupling of the tangent bundle $TM$ with the Lie algebra bundle $L$ (K.Mackenzie,2005, Definition 7.2.2) plays the crucial role in the classification of the transitive Lie algebroids for Lie algebra bundle $L$ with fixed finite dimensional Lie algebra $\rg$ as a fiber of $L$. Here we give a necessary and sufficient condition for existence such a coupling. Namely we define a new topology on the group $\Aut(\rg)$ of all automorphisms of Lie algebra $\rg$ and show that tangent bundle $TM$ can be coupled with the Lie algebra bundle $L$ if and only if the Lie algebra bundle L admits a local trivial structure with structural group endowed with such new topology.
- Добавил в систему: Мищенко Александр Сергеевич