# Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects

## Claude Roger

Address: Institut Camille Jordan, Université Claude Bernard Lyon I 21 avenue Claude Bernard, 69622 Villeurbanne Cedex, France

E-mail: roger@math.univ-lyon1.fr

Abstract: We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.

AMSclassification: primary 16E40; secondary 16E45, 17B56, 17B70, 53D17, 53D55, 58A50, 58D29, 81T70.

Keywords: supergeometry, odd symplectic manifolds, functional integral quantization, Graded Lie Algebras, Hochschild cohomology.