Generalized Lie bialgebras and Jacobi structures on Lie groups

Details Generalized Lie bialgebras and Jacobi structures on Lie groups Generalized Lie bialgebras and Jacobi structures on Lie groups

2001-02-21

arxiv.org/abs/math/0102171v1

Mathematics

Differential Geometry

32 pages

Scientific paper

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structures. We also propose a method to obtain generalized Lie bialgebras. It is a generalization of the Yang-Baxter equation method. Finally, we describe the structure of a compact generalized Lie bialgebra.

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