- Mohamed Barakat (University of Siegen, Germany)
- Max Horn (Justus Liebig University Giessen, Germany)

- group cohomology
- Lie algebra cohomology
- modules over path algebras
- constructive category theory
- coherent sheaf cohomology

- A
*short abstract*will appear on the permanent conference web page (see below) as soon as accepted.

- An
*extended abstract*will appear on the permanent conference web page (see below) as soon as accepted.

It will also appear on the proceedings that will be distributed during the meeting.

- A
consisting of*journal special issue**full papers*will be organized immediately after the meeting.

- If you would like to give a talk at ICMS, you need to submit
first a short abstract and then later an extended abstract. See
the guideline
for the details.

- After the meeting, the submission guideline for a journal special issue will be communicated to you by the session organizers.

### Group cohomology and efficient methods for group algebras of large p-groups.

David Green (Friedrich-Schiller-Universität Jena, Germany) (Slides)**Abstract**: How could one perform efficient calculations in the modular group algebra of a large p-group? For the p-group itself one would want to use a power-commutator presentation; I shall report on adapting this approach to the case of the group algebra. One intended application is the computation of the low-dimensional mod-2 cohomology groups of the sporadic finite simple group J_{4}. Parts are joint work with Robert Müller.### Endo-p-permutation modules: a computational approach via character theory

Caroline Lassueur (Technische Universität Kaiserslautern, Germany)**Abstract**: The endo-p-permutation and endo-trivial modules over the group algebra of a finite group over a field of prime characteristic are classes of modules with the nice property to beliftable to characteristic zero

. Thus the problem of their classification leads naturally to consider properties of the corresponding ordinary characters over the field of complex numbers. Through this approach many groups can be investigated using computational methods.### Constructing morphisms by diagram chases

Sebastian Posur (University of Siegen, Germany) (Slides)**Abstract**: In homological algebra, a method called diagram chasing is used to define important homomorphisms between modules over a ring. Examples of such morphisms are the connecting homomorphism in the snake lemma, and the differentials on the pages of a spectral sequence. In this talk, we discuss data structures that can be used to perform diagram chases constructively in the context of an arbitrary abelian category. These data structures are already implemented in our GAP-package CAP (Categories, Algorithms, and Programming). This is joint work with Mohamed Barakat and Sebastian Gutsche.### Test for infinite projective dimension

Øyvind Solberg (NTNU Trondheim, Norway)**Abstract**: Let Λ be a finite dimensional algebra over an algebraically closed field (or an admissible quotient of path algebra). An open problem for such algebras is the Finitistic Dimension Conjecture:The supremum of the projective dimension of all the finitely generated modules which have finite projective dimension is finite.

If one would know that this is true and one could compute the finitistic dimension of an algebra, one would have a finite test for showing that a module have infinite projective dimension. As this is still open, such a finite test is to my knowledge unknown.

We introduce the notion of a*matrix factorization*associated to all finitely generated Λ-modules, a*dimension vector invariant*of any finitely generated module over Λ and an abelian group G(Λ) in which all dimension vector invariants give rise to an element. We show that if the dimension vector invariant of a module M gives rise to a non-zero element in G(Λ), then the projective dimension of M is infinite. This is a finite test as it only involves computing a projective presentation of the module.