Group algebras whose groups of normalized units have exponent 4
We give a full description of locally finite -groups such that the normalized group of units of the group algebra over a field of characteristic has exponent .
Group algebras with centrally metabelian unit groups.
Given a field K of characteristic p > 2 and a finite group G, necessary and sufficient conditions for the unit group U(KG) of the group algebra KG to be centrally metabelian are obtained. It is observed that U(KG) is centrally metabelian if and only if KG is Lie centrally metabelian.
Group graded rings and smash products
Group laws and rings with normal bases.
Group Rings of Finite Representation Type.
Group Rings of Hypercyclic Groups.
Group Rings of Wild Representation Type
Group Rings Whose Units Form an FC-Group.
Group Rings Whose Units Form an FC-Group.
Group rings with FC-nilpotent unit groups.
Let U(RG) be the unit group of the group ring RG. Groups G such that U(RG) is FC-nilpotent are determined, where R is the ring of integers Z or a field K of characteristic zero.
Group Rings with Units Torsion Over the Center.
Groupe des classes de l'algèbre d'un groupe métacyclique.
Groupes totaux
Les « groupes totaux » sont les groupes pour lesquels la dimension du centre l’algèbre des invariants d’une algèbre simple centrale associée à un -cocycle sous l’action d’un relevé de l’action galoisienne à est constante quels que soient et . Dans cet article, nous montrons que les groupes quasi-CC (qui sont les groupes de centre cyclique et dont les centralisateurs des éléments hors du centre sont cycliques) sont totaux. Les groupes de type CC qui sont les groupes quasi-CC à centre trivial...
Group-Graded Rings and Modules.
Gruppenalgebren über nichtzyklischen p-Gruppen. I. Die Dieder- und die Quasidiedergruppen.
Hall algebras and quantum groups.
Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...
Hereditary endomorphism rings of mixed Abelian groups.
Hermitian and quadratic forms over Crossed-product orders
Hermitian and quadratic forms over local classical crossed product orders
Let R be a complete discrete valuation ring with quotient field K, L/K be a Galois extension with Galois group G and S be the integral closure of R in L. If a is a factor set of G with values in the group of units of S, then (L/K,a) (resp. Λ =(S/R,a)) denotes the crossed product K-algebra (resp. crossed product R -order in A). In this paper hermitian and quadratic forms on Λ -lattices are studied and the existence of at most two irreducible non-singular quadratic Λ -lattices is proved (Theorem 3.5)....