BV Algebras with Applications to Lie Bialgebras and Poisson Cohomology

2023/06/03 by Farinati, Marco A., Jancsa, A. Patricia
#16E45 #17B62 #17B63 #53D17 #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2306.02004

Abstract

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.

Related

• Gerstenhaber algebras and BV-algebras in Poisson geometry
• Poincare Duality For Smooth Poisson Algebras And BV Structure On Poisson Cohomology
• The BV-algebra of a Jacobi manifold
• Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry
• Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids