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

Claude Roger (2009)

Archivum Mathematicum

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.

Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories

Jolanta Słomińska (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.

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