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 HH^{1}(*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
HH^{1}(*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.