2000/08/15 by David Iglesias, Juan Carlos Marrero, Juan C. Marrero · 5 citations
Mathematics · Medicine · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.DG #math.SG #msc:17B62 #msc:53D10 #msc:53D17
paper · pdf · doi:10.1016/s0393-0440(01)00032-8
32 pages
arxiv created 2000/08/15 · openalex publication_date 2001/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.