BV Algebras with Applications to Lie Bialgebras and Poisson Cohomology

By using algebraic tools from differential Gerstenhaber algebras and Batalin-Vilkobisky algebras, we provide a new perspective on the modular class in Poisson geometry and the intrinsic biderivation of a Lie bialgebra. Furthermore, applications to Lie bialgebra cohomology and Poisson cohomology are given.