The Schur Multiplier of Some Finite Multiplicative Lie Algebras

被引：0

作者：

Kumar, Amit ^{[1
]}

Pal, Deepak ^{[1
]}

Kushwaha, Seema ^{[1
]}

Upadhyay, Sumit Kumar ^{[1
]}

机构：

[1] Indian Inst Informat Technol Allahabad, Dept Appl Sci, Prayagraj, India

来源：

JOURNAL OF LIE THEORY | 2024年 / 34卷 / 02期

关键词：

Multiplicative Lie algebra; Schur multiplier; exterior square; commutator;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify all the multiplicative Lie algebra structures on symmetric groups and alternating groups. We also determine the Schur multiplier and the Lie exterior square of some finite multiplicative Lie algebras. For a non abelian simple group K with trivial Schur multiplier, we see that the Schur multiplier of multiplicative Lie algebra K is trivial and the Lie exterior square of K is isomorphic to K with improper multiplicative Lie algebra structure.

引用

页码：423 / 436

页数：14

共 14 条

[1] Homology of multiplicative Lie rings [J].

Bak, A. ;

Donadze, G. ;

Inassaridze, N. ;

Ladra, M. .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2007, 208 (02) :761-777

[2]

Batten G., 1993, Dissertation

[3] On characterizing nilpotent Lie algebras by their multipliers [J].

Batten, P ;

Moneyhun, K ;

Stitzinger, E .

COMMUNICATIONS IN ALGEBRA, 1996, 24 (14) :4319-4330

[4] On the Schur multiplier of p-groups [J].

Ellis, G .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (09) :4173-4177

[5] ON 5 WELL-KNOWN COMMUTATOR IDENTITIES [J].

ELLIS, GJ .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1993, 54 :1-19

[6]

Karpilovsky G., 1987, LONDON MATH SOC MONO, V2

[7] Multiplicative Lie algebras and Schur multiplier [J].

Lal, Ramji ;

Upadhyay, Sumit Kumar .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2019, 223 (09) :3695-3721

[8]

MIAH SH, 1975, J LOND MATH SOC, V9, P549

[9] Characterizing finite p-groups by their Schur multipliers [J].

Niroomand, Peyman .

COMPTES RENDUS MATHEMATIQUE, 2012, 350 (19-20) :867-870

[10] CLASSIFICATION OF MULTIPLICATIVE LIE ALGEBRA STRUCTURES ON A FINITE GROUP [J].

Pandey, Mani Shankar ;

Upadhyay, Sumit Kumar .

COLLOQUIUM MATHEMATICUM, 2022, 168 (01) :25-34

← 1 2 →