Abstract

We review important examples of nonassociative algebras and geometry, specially Hom-associative algebras. The Hom-associative algebras first appeared in contexts related to physics. The study of q-deformations, based on deformed derivatives, of Heisenberg algebras, Witt and Virasoro algebras, and the quantum conformal algebras reveals a generalized Lie algebra structure in which the Jacobi identity is deformed by a linear map. Knwoing the fact that homological algebra is an important tool to study geometric objects, the aim of this talk is to develop homological tools to study this interesting class of nonassociative algebras. Specifically we introduce Hochschild and cyclic homology and cohomology for Hom-associative algebras. At the end we develop nonassociative differential calculus for Hom-associative algebras. This is Joint work with Ilya Shapiro and Serkan Sutlu.



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