Related papers: Wedderburn decomposition of commutative semisimple…

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components. We apply our work to obtain similar…

In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…

An algorithm for the explicit computation of a complete set of primitive central idempotents, Wedderburn decomposition and the automorphism group of the semisimple group algebra of a finite metabelian group is developed. The algorithm is…

We describe the primitive central idempotents of the group algebra over a number field of finite monomial groups. We give also a description of the Wedderburn decomposition of the group algebra over a number field for finite strongly…

In this paper, we introduce a method computing the primitive decomposition of idempotents of any semisimple finite group algebra based on its matrix representations and Wedderburn decomposition. Particularly, we use this method to calculate…

In this paper we give an explicit description of primitive central idempotents of rational group algebras of finite abelian groups using long presentation, and determine their Wedderburn decompositions.

Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.

In this article, we derive explicit combinatorial formulas, depending only on $q$, for the Wedderburn decomposition of the rational group algebras of the finite linear groups $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$.…

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of certain simple modules of the deformations of the subcharacter algebra of a finite group. For finite abelian groups, we prove that the…

In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…

Let $\mathcal G\simeq H\rtimes\Gamma$ be the semidirect product of a finite group $H$ and $\Gamma\simeq\mathbb Z_p$. Let $ F/\mathbb Q_p$ be a finite extension with ring of integers $\mathcal O_F$. Then the total ring of quotients $\mathcal…

In this article, we present a combinatorial formula for the Wedderburn decomposition of rational group algebras of nested GVZ $p$-groups, where $p$ is an odd prime. Using this formula, we derive an explicit combinatorial expression for the…

This is a survey paper on algorithms that have been developed during the last 25 years for the explicit computation of the structure of an associative algebra of finite dimension over either a finite field or an algebraic number field. This…

In this paper we obtain the Wedderburn-Artin decomposition of a semisimple group algebra associated to a direct product of finite groups. We also provide formulae for the number of all possible group codes, and their dimensions, that can be…

In this article, we present a concise combinatorial formula for efficiently determining the Wedderburn decomposition of rational group algebra associated with a split metacyclic $p$-group $G$, where $p$ is an odd prime. We also provide a…

We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…

We give a classification of semisimple and separable algebras in a multi-fusion category over an arbitrary field in analogy to Wedderben-Artin theorem in classical algebras. It turns out that, if the multi-fusion category admits a…

In this article, we present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra associated with an ordinary metacyclic $p$-group $G$, where $p$ is any prime. We also provide a formula for…

In this paper we develop a number of results and notions concerning Positivstellens\"atze for semirings (preprimes) of commutative unital real algebras. First we reduce the Archimedean Positivstellensatz for semirings to the corresponding…

In this article, we show explicitly the Wedderburn decomposition of the metacyclic group algebra $\mathbb F_qG$, where $G$ has a cyclic subgroup of index 2 and $\gcd(|G|,q)=1$. We also construct the complete set of central and left…