The Algebraic Structure of Finite Metabelian Group Algebras

被引：19

作者：

Bakshi, Gurmeet K. ^{[1
]}

Gupta, Shalini ^{[2
]}

Passi, Inder Bir S. ^{[1
,3
]}

机构：

[1] Panjab Univ, Ctr Adv Study Math, Chandigarh 160014, India

[2] Punjabi Univ, Dept Math, Patiala 147002, Punjab, India

[3] Indian Inst Sci Educ & Res, Mohali, India

来源：

COMMUNICATIONS IN ALGEBRA | 2015年 / 43卷 / 06期

关键词：

Automorphism group; Finite semisimple group algebra; Metabelian group; Primitive central idempotent; Wedderburn decomposition; 16S34; 20C05; 16K20; METACYCLIC GROUP;

D O I：

10.1080/00927872.2014.888566

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 illustrated with its application to the semisimple group algebra of an arbitrary metacyclic group, and certain indecomposable groups whose central quotient is the Klein four-group.

引用

页码：2240 / 2257

页数：18

共 9 条

[1]

Bakshi GK, 2013, J RAMANUJAN MATH SOC, V28, P141

[2] THE RATIONAL GROUP ALGEBRA OF A FINITE GROUP [J].

Bakshi, Gurmeet K. ;

Kulkarni, Ravindra S. ;

Passi, Inder Bir S. .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2013, 12 (03)

[3] Wedderburn decomposition of finite group algebras [J].

Broche, Osnel ;

del Rio, Angel .

FINITE FIELDS AND THEIR APPLICATIONS, 2007, 13 (01) :71-79

[4]

Curtis C. W., 2006, REPRESENTATION THEOR

[5] Some classes of semisimple group (and loop) algebras over finite fields [J].

Ferraz, Raul A. ;

Goodaire, Edgar G. ;

Milies, Cesar Polcino .

JOURNAL OF ALGEBRA, 2010, 324 (12) :3457-3469

[6]

Goodaire E. G., 1996, N HOLLAND MATH STUDI, V184

[7]

GOODAIRE EG, 1983, PUBL MATH-DEBRECEN, V30, P31

[8] On monomial characters and central idempotents of rational group algebras [J].

Olivieri, A ;

del Río, A ;

Simón, JJ .

COMMUNICATIONS IN ALGEBRA, 2004, 32 (04) :1531-1550

[9] The group of automorphisms of the rational group algebra of a finite metacyclic group [J].

Olivieri, Aurora ;

del Rio, A. ;

Simon, Juan Jacobo .

COMMUNICATIONS IN ALGEBRA, 2006, 34 (10) :3543-3567

← 1 →