Generalized Lie bialgebras and Jacobi structures on Lie groups

2001/02/21 by D. Iglesias, David Iglesias, Juan Carlos Marrero +3
Mathematics · Physics and Astronomy · #17B62 #22Exx #53D05 #53D10 #53D17 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:17B62 #msc:22Exx #msc:53D05 #msc:53D10 #msc:53D17

paper · pdf · doi:10.48550/arxiv.math/0102171

32 pages

arxiv created 2001/02/21 · openalex publication_date 2001/02/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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