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The modular characters of the twisted Chevalley group 2D4(2) over GF2.

Ibrahim A. I. Suleiman (1995)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we calculate the 2-modular character table of the twisted Chevalley group 2D4(2) using computer techniques available in an algebra package called Meat-Axe. This package is now available in Mu'tah University as well as other universities such as Birmingham University in the UK and Aachen University in Germany. The determination of this character table will be a contribution to modular calculations of various simple groups.

The periodicity conjecture for blocks of group algebras

Karin Erdmann, Andrzej Skowroński (2015)

Colloquium Mathematicae

We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.

Thick subcategories of the stable module category

D. Benson, Jon Carlson, Jeremy Rickard (1997)

Fundamenta Mathematicae

We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...

Twisted group rings of strongly unbounded representation type

Leonid F. Barannyk, Dariusz Klein (2004)

Colloquium Mathematicae

Let S be a commutative local ring of characteristic p, which is not a field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and S λ G a twisted group ring of the group G and of the ring S with a 2-cocycle λ ∈ Z²(G,S*). Denote by I n d m ( S λ G ) the set of isomorphism classes of indecomposable S λ G -modules of S-rank m. We exhibit rings S λ G for which there exists a function f λ : ℕ → ℕ such that f λ ( n ) ≥ n and I n d f λ ( n ) ( S λ G ) is an infinite set for every natural n > 1. In special cases f λ ( ℕ ) contains every natural number m >...

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