Stable equivalences of Morita type for self-injective algebras and p-groups.
Stacks of group representations
We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group , the derived and the stable categories of representations of a subgroup can be constructed out of the corresponding category for by a purely triangulated-categorical construction, analogous to étale extension in algebraic geometry. In the case of finite groups, we then use descent methods to investigate...
Staircases in .
Standard character condition for table algebras.
Strongly prime radical of group algebras.
Structure and detection theorems for -modules
Structure of the Unit Group of FD10
2000 Mathematics Subject Classification: 16U60, 20C05.The structure of the unit group of the group algebra FD10 of the dihedral group D10 of order 10 over a finite field F has been obtained.Supported by National Board of Higher Mathematics, DAE, India.
Structure of the unit group of the group algebras of non-metabelian groups of order 128
We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.
Structure of unitary groups over finite group rings and its application
In this paper, we determine all the normal forms of Hermitian matrices over finite group rings , where , is a commutative -group with order . Furthermore, using the normal forms of Hermitian matrices, we study the structure of unitary group over through investigating its BN-pair and order. As an application, we construct a Cartesian authentication code and compute its size parameters.
Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....
SU (2)-representation spaces for two-bridge knot groups.
Subgroups and modular representations of finite quasisimple groups
Subgroups of odd depth—a necessary condition
This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with -entries to have maximal rank. The entries of the matrix...
Subgroups of the basic subgroup in a modular group ring
Subgroups with projective abelianization and trivial multiplicator.
Subpair multiplicities in finite groups.
Summands of finite group algebras
We study the inverse problem of the determination of a group algebra from the knowledge of its Wedderburn decomposition. We show that a certain class of matrix rings always occur as summands of finite group algebras.
Supersolvable Automorphism Groups of Solvable Groups.
Supersymmetry classes of tensors
We introduce the notion of a supersymmetry class of tensors which is the ordinary symmetry class of tensors with a natural ℤ₂-gradation. We give the dimensions of even and odd parts of this gradation as well as their natural bases. Also we give a necessary and sufficient condition for the odd or even part of a supersymmetry class to be zero.
Sur la cohomologie de la compactification des variétés de Deligne-Lusztig
Nous étudions la cohomologie de la compactification des variétés de Deligne-Lusztig associées aux éléments de Coxeter. Nous présentons une conjecture des relations entre la cohomologie de la variété et la cohomologie de ses compactifications partielles. Nous prouvons la conjecture dans le cas du groupe linéaire général.