Addendum to “Hochschild cohomology of skew group rings and invariants”
Biquaternion algebras and quartic extensions
Classification of the simple modules of the quantum Weyl algebra and the quantum plane
Construction of Auslander-Gorenstein local rings as Frobenius extensions
Starting from an arbitrary ring R we provide a systematic construction of ℤ/nℤ-graded rings A which are Frobenius extensions of R, and show that under mild assumptions, A is an Auslander-Gorenstein local ring if and only if so is R.
Decomposition of Mal'cev-Neumann division algebras with involution.
Dimension injective des produits croisés.
Endomorphism rings of -comodule algebras.
Extensions of nilpotent blocks.
Finite groups of OTP projective representation type
Let K be a field of characteristic p > 0, K* the multiplicative group of K and a finite group, where is a p-group and B is a p’-group. Denote by a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module V and a simple...
Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic
Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...
Finite-dimensional twisted group algebras of semi-wild representation type
Let G be a finite group, K a field of characteristic p > 0, and the twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for to be of semi-wild representation type in the sense of Drozd. We also introduce the concept of projective K-representation type for a finite group (tame, semi-wild, purely semi-wild) and we exhibit finite groups of each type.
Gelfand-Kirillov dimension in some crossed products.
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...
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)....
Hochschild Cohomology of skew group rings and invariants
Let A be a k-algebra and G be a group acting on A. We show that G also acts on the Hochschild cohomology algebra HH ⊙ (A) and that there is a monomorphism of rings HH ⊙ (A) G→HH ⊙ (A[G]). That allows us to show the existence of a monomorphism from HH ⊙ (Ã) G into HH ⊙ (A), where à is a Galois covering with group G.
Indecomposable -lattices for a class of metabelian groups
Non-commutative separability and group actions.
We give conditions for the skew group ring S * G to be strongly separable and H-separable over the ring S. In particular we show that the H-separability is equivalent to S being central Galois extension. We also look into the H-separability of the ring S over the fixed subring R under a faithful action of a group G. We show that such a chain: S * G H-separable over S and S H-separable over R cannot occur, and that the centralizer of R in S is an Azumaya algebra in the presence of a central element...
Notes on Galois extensions with inner Galois groups.
On a class of free Galois extensions.