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Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects. (English) Zbl 1212.58004

Summary: 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.

MSC:

58A50 Supermanifolds and graded manifolds
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16E45 Differential graded algebras and applications (associative algebraic aspects)
17B56 Cohomology of Lie (super)algebras
17B70 Graded Lie (super)algebras
53D17 Poisson manifolds; Poisson groupoids and algebroids
53D55 Deformation quantization, star products
81T70 Quantization in field theory; cohomological methods
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