by Asashiba, Hideto

We shall show that every stable equivalence (functor) between representation-finite self-injective algebras not of type (D
_3m
,s/3,1) with m≥2, 3∤s lifts to a standard derived equivalence. This implies that all stable equivalences between these algebras are of Morita type.

DOI: 10.1023/B:ALGE.0000003543.02426.4d
Print publication date: 10/1/2003
View article on SpringerLink

by Opolka, Hans

A central pair over a field k of characteristic 0 consists of a finite Abelian group which is equipped with a central 2-cocycle with values in the multiplicative group k
^* of k. In this paper we use specific central pairs to construct a class of projective representations of the absolute Galois group G

_k
of k and if k is a number field we investigate the liftings of these projective representations to linear representations of G

_k
. In particular we relate these linear representations to automorphic representations. It turns out that some of these automorphic representations correspond to certain indefinite modular forms already constructed by E. Hecke.

DOI: 10.1023/B:ALGE.0000003541.31684.62
Print publication date: 10/1/2003
View article on SpringerLink

by Sasaki, Hiroki

We calculate the mod7 cohomology algebra of the Held simple group, whose Sylow 7-subgroups are extraspecial of order 7³ and exponent 7. Our method depends on the analysis of the Carlson module of a regular class belonging to a system of parameters.

DOI: 10.1023/B:ALGE.0000003542.64788.60
Print publication date: 10/1/2003
View article on SpringerLink

by Kashina, Yevgenia

In this paper we classify all nontrivial semisimple Hopf algebras of dimension 2
<sup>n

+1</sup> with the group of grouplikes isomorphic to ℤ<sub>2

n−1</sub>×ℤ₂. Moreover, we extend some results on irreducible representations from groups to semisimple Hopf algebras and prove that certain semisimple Hopf algebras, including the ones classified in this paper, satisfy the generalized power map property.

DOI: 10.1023/B:ALGE.0000003540.74953.97
Print publication date: 10/1/2003
View article on SpringerLink