Capable Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field

被引：14

作者：

Niroomand, Peyman ^{[1
]}

Johari, Farangis ^{[2
]}

Parvizi, Mohsen ^{[2
]}

机构：

[1] Damghan Univ, Sch Math & Comp Sci, Damghan, Iran

[2] Ferdowsi Univ Mashhad, Dept Pure Math, Mashhad, Iran

来源：

LINEAR & MULTILINEAR ALGEBRA | 2019年 / 67卷 / 03期

关键词：

Capability; Schur multiplier; generalized Heisenberg Lie algebras; stem Lie algebras; SCHUR MULTIPLIER; CLASSIFICATION; CAPABILITY; COVERS;

D O I：

10.1080/03081087.2018.1425356

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given.

引用

页码：542 / 554

页数：13

共 20 条

[1] On covers of Lie algebras [J].

Batten, P ;

Stitzinger, E .

COMMUNICATIONS IN ALGEBRA, 1996, 24 (14) :4301-4317

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

Batten, P ;

Moneyhun, K ;

Stitzinger, E .

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

[3] GROUPS OCCURRING AS CENTER FACTOR GROUPS [J].

BEYL, FR ;

FELGNER, U ;

SCHMID, P .

JOURNAL OF ALGEBRA, 1979, 61 (01) :161-177

[4] ON SCHUR MULTIPLIERS OF LIE ALGEBRAS AND GROUPS OF MAXIMAL CLASS [J].

Bosko, Lindsey R. .

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2010, 20 (06) :807-821

[5] Six-dimensional nilpotent Lie algebras [J].

Cicalo, Serena ;

de Graaf, Willem A. ;

Schneider, Csaba .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (01) :163-189

[6] Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2 [J].

de Graaf, Willem A. .

JOURNAL OF ALGEBRA, 2007, 309 (02) :640-653

[7] A NON-ABELIAN TENSOR PRODUCT OF LIE-ALGEBRAS [J].

ELLIS, GJ .

GLASGOW MATHEMATICAL JOURNAL, 1991, 33 :101-120

[8]

Gong M.-P., 1998, THESIS

[9]

Hall P, 1940, J REINE ANGEW MATH, V182, P130

[10] On characterizing nilpotent lie algebras by their multipliers, t(L) = 3,4,5,6 [J].

Hardy, P ;

Stitzinger, E .

COMMUNICATIONS IN ALGEBRA, 1998, 26 (11) :3527-3539

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