Generalized Lie bialgebroids and Jacobi structures
By D. Iglesias, Juan Carlos Marrero. 2000
115 citations recorded by the source corpus.
Abstract 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.
Subfields: Algebra and Number Theory, Mathematical Physics, Pathology and Forensic Medicine
View Paper: https://www.semanticscholar.org/paper/3ddcf4f5354a91bc187a2234b7d244d57a984cae
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In Algebra and Number Theory
In Mathematical Physics
In Pathology and Forensic Medicine
Citations in the corpus
- Lie Brackets on Affine Bundles (2002, background): “This construction for generalized Lie algebroids can be found in [6].”
- Calculus on Lie algebroids, Lie groupoids and Poisson manifolds (2008, background): “Marrero have introduced a generalization of that notion in relation with Jacobi manifolds [21].”
- Contact manifolds and generalized complex structures (2004, background): “(α1,g1), (1) for any (Xj,fj) + (αj,gj) ∈ Γ(E1(M)) with j = 1,2. The skew-symmetric version of [·,·]E1(M) was introduced in [Wa00]. One can notice that de is nothing but the operator d(0,1) introduced [IM01]. Moreover, E1(M) is an example of the so-called Courant-Jacobi algebroid (see [GM03]). Definit”