Cohomology and deformations of twisted tensor product algebras

Abstract: We will introduce some homological techniques for understanding deformations of twisted tensor product algebras. We will first describe a general construction of twisted tensor product resolution. We will
then focus on the special cases of group actions and Hopf algebra actions on Koszul algebras, with the goal of understanding graded deformations of the corresponding twisted tensor product algebras. These include many classes of examples of interest, such as symplectic reflection algebras and infinitesimal Hecke algebras.