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Generalized Lie bialgebroids and Jacobi structures

✍ Scribed by David Iglesias; Juan C. Marrero

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 182 KB
Volume: 40
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(01)00032-8

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✦ Synopsis

The notion of a generalized Lie bialgebroid (a generalization of the notion of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has associated a canonical generalized Lie bialgebroid. As a kind of converse, we prove that a Jacobi structure can be defined on the base space of a generalized Lie bialgebroid. We also show that it is possible to construct a Lie bialgebroid from a generalized Lie bialgebroid and, as a consequence, we deduce a duality theorem. Finally, some special classes of generalized Lie bialgebroids are considered: triangular generalized Lie bialgebroids and generalized Lie bialgebras.

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