Derived invariance of operations in Hochschild theory

Abstract: In this talk, I will introduce Hochschild homology and cohomology, together with the well-known operations cup product and Gerstenhaber bracket, and the not-so-known cap product and Connes differential. I will explain how all these operations can be interpreted inside the derived category of the algebra which allows proving derived invariance of the whole structure, known as a Tamarkin-Tsygan calculus or a differential calculus. Finally, I will show how this construction is functorial in the algebra using cyclic homology, and give an example showing that the Tamarkin-Tsygan calculus is not a complete derived invariant, by means of quivers and the Coxeter polynomial. This is joint work with Bernhard Keller.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

Series comments: Please email Yu-Shen Lin (yslin0221@gmail.com) for password or adding to the email list.