scholarly journals An algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package wedderga

2009 ◽  
Vol 44 (5) ◽  
pp. 507-516 ◽  
Author(s):  
Gabriela Olteanu ◽  
Ángel del Río
Keyword(s):  
Semisimple Group ◽  
Group Algebras ◽  
Wedderburn Decomposition

scholarly journals Finite semisimple group algebra of a normally monomial group

2019 ◽  
Vol 29 (01) ◽  
pp. 159-177 ◽  
Author(s):  
Shalini Gupta ◽  
Sugandha Maheshwary
Keyword(s):  
Group Algebra ◽  
Algebraic Structure ◽  
Automorphism Groups ◽  
Semisimple Group ◽  
Group Algebras ◽  
Wedderburn Decomposition ◽  
Monomial Group

In this paper, the complete algebraic structure of the 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 algebras of various normally monomial groups. The automorphism groups of these group algebras are also determined.

scholarly journals Finite Metabelian Group Algebras

2016 ◽  
Vol 17 ◽  
pp. 30-38
Author(s):  
Shalini Gupta
Keyword(s):  
Automorphism Group ◽  
Cyclic Group ◽  
Group Algebra ◽  
Algebraic Structure ◽  
Metabelian Group ◽  
Semisimple Group ◽  
Group Algebras ◽  
Wedderburn Decomposition ◽  
Central Quotient

Given a finite metabelian group G, whose central quotient is abelian (not cyclic) group of order p2, p odd prime, the objective of this paper is to obtain a complete algebraic structure of semisimple group algebra Fq[G] in terms of primitive central idempotents, Wedderburn decomposition and the automorphism group.

On *-clean non-commutative group rings

2016 ◽  
Vol 15 (08) ◽  
pp. 1650150 ◽  
Author(s):  
Hongdi Huang ◽  
Yuanlin Li ◽  
Gaohua Tang
Keyword(s):  
Finite Field ◽  
Local Ring ◽  
Group Algebra ◽  
Rational Numbers ◽  
Semisimple Group ◽  
Group Algebras ◽  
Group Rings ◽  
Dihedral Groups ◽  
Commutative Local Ring ◽  
Generalized Quaternion

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups [Formula: see text], and the generalized quaternion groups [Formula: see text] with standard involution ∗. For the non-semisimple group algebra case, we characterize the ∗-cleanness of [Formula: see text] with a prime [Formula: see text], and [Formula: see text] with [Formula: see text], where [Formula: see text] is a commutative local ring. For the semisimple group algebra case, we investigate when [Formula: see text] is ∗-clean, where [Formula: see text] is the field of rational numbers [Formula: see text] or a finite field [Formula: see text] and [Formula: see text] or [Formula: see text].

scholarly journals Unit Groups of Semisimple Group Algebras of Abelianp-Groups over a Field

1997 ◽  
Vol 188 (2) ◽  
pp. 580-589 ◽  
Author(s):  
Nako A. Nachev ◽  
Todor Zh. Mollov
Keyword(s):  
Semisimple Group ◽  
Group Algebras

scholarly journals On Idempotents and the Number of Simple Components of Semisimple Group Algebras

2015 ◽  
Vol 19 (2) ◽  
pp. 315-333
Author(s):  
Gabriela Olteanu ◽  
Inneke Van Gelder
Keyword(s):  
Semisimple Group ◽  
Group Algebras

On the dimension of ideals in group algebras, and group codes

2020 ◽  
pp. 2250024
Author(s):  
E. J. García-Claro ◽  
H. Tapia-Recillas
Keyword(s):  
Minimum Distance ◽  
Semisimple Group ◽  
Group Algebras ◽  
Mds Codes ◽  
Hamming Weight ◽  
Group Codes ◽  
Minimal Polynomials ◽  
Principal Ideals ◽  
Regular Representations ◽  
Abelian Code

Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of semisimple group algebras, to compute, for any abelian code, an element with Hamming weight equal to its dimension. Finally, to get bounds on the minimum distance of certain MDS group codes. A relation between a class of group codes and MDS codes is presented. Examples illustrating the main results are provided.

STRUCTURE OF SOME CLASSES OF SEMISIMPLE GROUP ALGEBRAS OVER FINITE FIELDS

2014 ◽  
Vol 51 (6) ◽  
pp. 1605-1614 ◽  
Author(s):  
Neha Makhijani ◽  
Rajendra Kumar Sharma ◽  
J.B. Srivastava
Keyword(s):  
Finite Fields ◽  
Semisimple Group ◽  
Group Algebras

scholarly journals A classification of exceptional components in group algebras over abelian number fields

2016 ◽  
Vol 15 (05) ◽  
pp. 1650092
Author(s):  
Andreas Bächle ◽  
Mauricio Caicedo ◽  
Inneke Van Gelder
Keyword(s):  
Finite Group ◽  
Unit Group ◽  
Number Fields ◽  
Group Algebras ◽  
Matrix Rings ◽  
Division Rings ◽  
Wedderburn Decomposition ◽  
A Finite Group

When considering the unit group of [Formula: see text] ([Formula: see text] the ring of integers of an abelian number field [Formula: see text] and a finite group [Formula: see text]) certain components in the Wedderburn decomposition of [Formula: see text] cause problems for known generic constructions of units; these components are called exceptional. Exceptional components are divided into two types: type 1 is division rings, type 2 is [Formula: see text]-matrix rings. For exceptional components of type 1 we provide infinite classes of division rings by describing the seven cases of minimal groups (with respect to quotients) having those division rings in their Wedderburn decomposition over [Formula: see text]. We also classify the exceptional components of type 2 appearing in group algebras of a finite group over number fields [Formula: see text] by describing all 58 finite groups [Formula: see text] having a faithful exceptional Wedderburn component of this type in [Formula: see text].

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