Tuesday, October 17, 14:00, 7.527.

Lleonard Rubio y Degrassi (City, University of London)
On Hochschild cohomology and global/local structures.

Abstract:
In this talk I will discuss the interplay between the local and the global invariants in modular representation theory with a focus on the first Hochschild cohomology HH¹(B) of a block algebra B. In particular, I will show the compatibility between r-integrable derivations and stable equivalences of Morita type. I will also show that if HH¹(B) is a simple Lie algebra such that B has a unique isomorphism class of simple modules, then B is nilpotent with an elementary abelian defect group P of order at least 3. The second part is joint work with M. Linckelmann.