Triangular generalized Lie bialgebroids: Homology and cohomology theories
Volume 54 / 2001
Banach Center Publications 54 (2001), 111-133
MSC: Primary 53D10, 53D17; Secondary 17B62.
DOI: 10.4064/bc54-0-8
Abstract
Triangular generalized Lie bialgebroids are a generalization of triangular Lie bialgebroids in the sense of Mackenzie and Xu. For this type of structures two homology and cohomology theories are considered. Moreover, we prove that the vanishing of a certain cohomo\-logy class, which we will call the modular class, implies the existence of a duality between these homology and cohomology theories. As a consequence, we recover some previous results for unimodular Poisson and Jacobi manifolds and unimodular triangular Lie bialgebroids.
