Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

Markus Linckelmann
University of Aberdeen
On Hochschild cohomology of block algebras
DMV Tagung 2011 - Köln, 19. - 22. September
The Hochschild cohomology of a finite dimensional algebra A over a field is a graded-commutative
k-algebra which encodes cohomological information on A viewed as a bimodule. In the context of
block algebras (that is, indecomposable direct factors of finite group algebras), some of the finiteness
conjectures in that area, such as Donovan’s, would imply that for a fixed defect group there should be
only finitely many isomorphism classes of Hochschild cohomology algebras of blocks with a fixed defect
group. Using recent work of Benson and Symonds on the Castelnuovo-Mumford regularity of finite group
cohomology, we show that there are only finitely many Hilbert series of Hochschild cohomology algebras
of blocks with a fixed defect. This extends in particular a classic result of Brauer and Feit bounding the
dimension of the degree zero component of Hochschild cohomology in terms of the defect. The methods
used range from standard block theory to local cohomology in commutative algebra. This is joint work
with Radha Kessar.
Maurizio Martino
Universität Bonn
Partial KZ functors for Cherednik algebras
Rational Cherednik algebras were introduced by Etingof and Ginzburg as a family of algebras which
deform the coordinate rings of certain quotient singularities. An important feature of these algebras is
their connection to finite-dimensional Hecke algebras, via the KZ functor. I will describe "partial" versions
of these, which arise from normalisers of parabolic subalgebras. As an application, I will explain how to
use these to re-prove a theorem of P.Shan, which categorifies certain higher level Fock spaces. This is
joint work with I.Gordon.
Volodymyr Mazorchuk
Uppsala University
2-representations of finitary 2-categories
In the talk I will try to describe how one constructs and compares principal and cell 2-representations of
finitary 2-categories. Based on a joint work with Vanessa Miemietz.
Vanessa Miemietz
University of East Anglia, Norwich
Homological algebras for GL_2
For the general linear group of rank two over an algebraically closed field of positive characteristic, we
explicitly describe various extension algebras related to its representation theory. This is based on a
2-functorial and combinatorial approach to construct all rational representations from just the base field
and a notion of homological duality for 2-functors. It is joint work with Will Turner.
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