by

DOI: 10.1023/A:1017328408299
Print publication date: 12/1/2000
View article on SpringerLink

by Plesken, W.

Automorphism groups of Hadamard matrices are investigated from the point of view of integral representation theory. Interesting examples involving the Mathieu groups M
₁₂ and M
₂₄ and the Leech lattice are dicussed.

DOI: 10.1023/A:1009958227635
Print publication date: 12/1/2000
View article on SpringerLink

by Keller, Bernhard

We present a new and explicit method for lifting a tilting complex to a bimodule complex. The key ingredient of our method is the notion of a strong homotopy action in the sense of Stasheff.

DOI: 10.1023/A:1009954126727
Print publication date: 12/1/2000
View article on SpringerLink

by Lehrer, G. I.

An explicit formula is given for the graded trace of a permutation acting on the cohomology of the space of configurations of n ordered distinct points of R

^d
. This is applied to determine the top and total cohomology as modules for the symmetric group, and to locate the occurrence of the alternating representation.

DOI: 10.1023/A:1009906210797
Print publication date: 12/1/2000
View article on SpringerLink

by Linchenko, V.; Montgomery, S.

We prove a version of the Frobenius–Schur theorem for a finite-dimensional semisimple Hopf algebra H over an algebraically closed field; if the field has characteristic p not 0, H is also assumed to be cosemisimple. Then for each irreducible representation V of H, we define a Schur indicator for V, which reduces to the classical Schur indicator when H is the group algebra of a finite group. We prove that this indicator is 0 if and only if V is not self-dual. If V is self dual, then the indicator is positive (respectively, negative) if and only if V admits a nondegenerate bilinear symmetric (resp., skew-symmetric) H-invariant form. A more general result is proved for algebras with involution.

DOI: 10.1023/A:1009949909889
Print publication date: 12/1/2000
View article on SpringerLink

by Benson, D. J.; Krause, H.

Let G be a finite group and k an algebraically closed field of characteristic p. Let F

_U
be the Rickard idempotent k G-module corresponding to the set U of subvarieties of the cohomology variety V

_G
which are not irreducible components. We show that F

_U
is a finite sum of generic modules corresponding to the irreducible components of V

_G
. In this context, a generic module is an indecomposable module of infinite length over k G but finite length as a module over its endomorphism ring.

DOI: 10.1023/A:1009997808980
Print publication date: 12/1/2000
View article on SpringerLink

by Carlson, Jon F.; Thévenaz, Jacques

We prove that the group T(G) of endo-trivial modules for a noncyclic finite p-group G is detected on restriction to the family of subgroups which are either elementary Abelian of rank 2 or (almost) extraspecial. This result is closely related to the problem of finding the torsion subgroup of T(G). We give the complete structure of T(G) when G is dihedral, semi-dihedral, or quaternion.

DOI: 10.1023/A:1009988424910
Print publication date: 12/1/2000
View article on SpringerLink

by

DOI: 10.1023/A:1017317008071
Print publication date: 12/1/2000
View article on SpringerLink

by

DOI: 10.1023/A:1017240721158
Print publication date: 12/1/2000
View article on SpringerLink