Separable subalgebras of a class of Azumaya algebras.
Severi-Brauer varieties of semidirect product algebras.
Skew group rings which are Galois.
Smash products, group actions and group graded rings.
Some algebraic applications of graded categorical group theory.
Some correspondences for Galois skew group rings.
Strongly groupoid graded rings and cohomology
We interpret the collection of invertible bimodules as a groupoid and call it the Picard groupoid. We use this groupoid to generalize the classical construction of crossed products to what we call groupoid crossed products, and show that these coincide with the class of strongly groupoid graded rings. We then use groupoid crossed products to obtain a generalization from the group graded situation to the groupoid graded case of the bijection from a second cohomology group, defined by the grading...
The basic construction from the conditional expectation on the quantum double of a finite group
Let be a finite group and a subgroup. Denote by (or ) the crossed product of and (or ) with respect to the adjoint action of the latter on the former. Consider the algebra generated by and , where we regard as an idempotent operator on for a certain conditional expectation of onto . Let us call the basic construction from the conditional expectation . The paper constructs a crossed product algebra , and proves that there is an algebra isomorphism between and .
The Boolean algebra and central Galois algebras.
The Boolean algebra of Galois algebras.
The Galois algebras and the Azumaya Galois extensions.
The Galois extensions induced by idempotents in a Galois algebra.
The general Ikehata theorem for -separable crossed products.
The invariant subrings of DeMeyer-Kanzaki Galois extensions.
The parametrization of interior algebras.
Twisted group rings of strongly unbounded representation type
Let S be a commutative local ring of characteristic p, which is not a field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and a twisted group ring of the group G and of the ring S with a 2-cocycle λ ∈ Z²(G,S*). Denote by the set of isomorphism classes of indecomposable -modules of S-rank m. We exhibit rings for which there exists a function such that and is an infinite set for every natural n > 1. In special cases contains every natural number m >...
Valuations and group algebras
Глобализация локальных действий коалгебр.
Изоморфные скрещенные произведения групп и первичных колец
О рациональном замыкании групповой алгебры линейно упорядоченной группы в теле рядов Мальцева.