EVENT DETAILS AND ABSTRACT

Title: Operations on cochains and (pre) CY algebras
Speaker: Boris Tsygan
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

As it is known from the early sixties (Gerstenhaber), deformations of an associative algebra are MC elements of the dg Lie algebra of Hochschild cochains. More recently, deformations of a Frobenius algebra are governed by the Lie algebra of cyclic cochains (Connes, Flato and Sternheimer). Frobenius algebras are partial cases of a right CY algebra. There is also a dual notion of a left CY algebra. Their common generalization is a pre-CY algebra (Kontsevich-Vlassopoulos). A pre-CY algebra structure is a MC element in the dg Lie algebra of higher Hochschild cochains. The latter is, in essence, the algebra of cyclic cochains of some auxiliary Frobenius algebra. Higher Hochschild chains are also defined, but they are equivalent to usual Hochschild chains. This equivalence is itself interesting, giving rise to cyclotomic methods. I will outline the theory, following the above authors and Waikit Yeung.