A short note on Wedderburn decomposition of a group algebra

被引：1

作者：

Mittal, Gaurav ^{[1
,2
]}

Sharma, R. K. ^{[3
]}

机构：

[1] Def Res & Dev Org, Near Metcalfe House, New Delhi 110054, India

[2] Indian Inst Technol Roorkee, Dept Math, Roorkee 247667, India

[3] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India

来源：

EXAMPLES AND COUNTEREXAMPLES | 2023年 / 3卷

关键词：

Wedderburn decomposition; Unit group; Representation theory; SEMISIMPLE GROUP-ALGEBRA;

D O I：

10.1016/j.exco.2023.100105

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we extend the result of Mittal and Sharma (Bull. Korean Math. Soc. 2022) on Wedderburn decomposition (WD) of a finite semisimple group algebra. It is known that, under certain conditions, WD of a finite semisimple group algebra FqG can be computed from WD of its subalgebra Fq(G/H), where H is a normal subgroup of G of prime order and q=pk for some prime p and positive integer k. We extend this result to any normal subgroup H of G of order n.

引用

页数：2

共 50 条

[31] Derivation algebra and automorphism group of generalized topological N=2 superconformal algebra
Yang, Hengyun
Yu, Yafeng
Yao, Tingfu
FRONTIERS OF MATHEMATICS IN CHINA, 2013, 8 (04) : 973 - 986
[32] On the Lower Bound of the Derived Length of the Unit Group of a Nontorsion Group Algebra
Tibor Juhász
Gregory T. Lee
Sudarshan K. Sehgal
Ernesto Spinelli
Algebras and Representation Theory, 2020, 23 : 457 - 466
[33] On the Lower Bound of the Derived Length of the Unit Group of a Nontorsion Group Algebra
Juhasz, Tibor
Lee, Gregory T.
Sehgal, Sudarshan K.
Spinelli, Ernesto
ALGEBRAS AND REPRESENTATION THEORY, 2020, 23 (02) : 457 - 466
[34] Computing the automorphism group of a solvable Lie algebra
Eick, B
LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 382 : 195 - 209
[35] On the order of unitary subgroup of the modular group algebra
Makhijani, Neha
Sharma, R. K.
Srivastava, J. B.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (08)
[36] On the normal complement problem of finite group algebra
Upadhyay, Diksha
Chandra, Harish
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2023, 16 (11)
[37] Relationship between Codes and Idempotents in a Dihedral Group Algebra
Vedenev, K. V.
Deundyak, V. M.
MATHEMATICAL NOTES, 2020, 107 (1-2) : 201 - 216
[38] THE STRUCTURE OF THE UNIT GROUP OF THE GROUP ALGEBRA OF PAULI'S GROUP OVER ANY FIELD OF CHARACTERISTIC 2
Gildea, Joe
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2010, 20 (05) : 721 - 729
[39] Relationship between Codes and Idempotents in a Dihedral Group Algebra
K. V. Vedenev
V. M. Deundyak
Mathematical Notes, 2020, 107 : 201 - 216
[40] The one-sided cycle shuffles in the symmetric group algebra
Grinberg, Darij
Lafreniere, Nadia
ALGEBRAIC COMBINATORICS, 2024, 7 (02): : 275 - 326

← 1 2 3 4 5 →