Pre-talk title: Hochschild cohomology and finite-dimensional algebras
Pre-talk abstract: In the pre-talk, I will go over Hochschild cohomology and its Gerstenhaber algebra structure. I will also discuss how path algebras give us a description of finite-dimensional algebras and monomial algebras more generally.
Title: Hochschild cohomology of triangular monomial algebras
Abstract: The Hochschild cohomology of an algebra is itself a commutative graded algebra where the multiplication is given by the cup product, and with the Gerstenhaber bracket, this is a Gerstenhaber algebra. Monomial algebras can be realized as quotients of path algebras and have a nice resolution described by Bardzell in 1997. This has led to a substantial body of work describing the Hochschild cohomology of certain classes of monomial algebras and their Gerstenhaber algebra structure. In this talk, I will discuss the Hochschild cohomology of triangular monomial algebras and their cup product. This discussion is based on joint work with Dalia Artenstein, Janina Letz, Sibylle Schroll, and Andrea Solotar.