THE CLASSIFICATION OF NATURALLY GRADED p-FILIFORM LEIBNIZ ALGEBRAS

被引：19

作者：

Camacho, L. M. ^{[1
]}

Gomez, J. R. ^{[1
]}

Gonzalez, A. J. ^{[2
]}

Omirov, B. A.

机构：

[1] Univ Seville, Dept Matemat Aplicada 1, Seville, Spain

[2] Univ Extremadura, Dept Matemat, Badajoz, Spain

来源：

COMMUNICATIONS IN ALGEBRA | 2011年 / 39卷 / 01期

关键词：

Characteristic sequence; Leibniz algebra; Lie algebra; Natural gradation; Nilpotence; p-Filiformlicity; LIE-ALGEBRAS; DIMENSION;

D O I：

10.1080/00927870903451900

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present article the classification of n-dimensional naturally graded p-filiform (1 <= p <= n - 4) Leibniz algebras is obtained. A splitting of the set of naturally graded Leibniz algebras into the families of Lie and non Lie Leibniz algebras by means of characteristic sequences (isomorphism invariants) is proved.

引用

页码：153 / 168

页数：16

共 10 条

[1] Varieties of nilpotent complex Leibniz algebras of dimension less than five# [J].

Albeverio, S ;

Omirov, BA ;

Rakhimov, IS .

COMMUNICATIONS IN ALGEBRA, 2005, 33 (05) :1575-1585

[2]

AYUPOV SA, 2001, SIBERIAN MATH J, V42, P18

[3]

Cabezas JM, 2005, J LIE THEORY, V15, P379

[4] NATURALLY GRADED 2-FILIFORM LEIBNIZ ALGEBRAS [J].

Camacho, L. M. ;

Gomez, J. R. ;

Gonzalez, A. J. ;

Omirov, B. A. .

COMMUNICATIONS IN ALGEBRA, 2010, 38 (10) :3671-3685

[5] Non-abelian tensor product of Leibniz algebras and an exact sequence in Leibniz homology [J].

Casas, JM ;

Ladra, M .

COMMUNICATIONS IN ALGEBRA, 2003, 31 (09) :4639-4646

[6] Versal Deformations of Leibniz Algebras [J].

Fialowski, Alice ;

Mandal, Ashis ;

Mukherjee, Goutam .

JOURNAL OF K-THEORY, 2009, 3 (02) :327-358

[7]

Goze M., 1996, MATH ITS APPL, V361

[8]

Loday J.-L., 1993, ENSEIGN MATH, V39, P269

[9] Leibniz representations of Lie algebras [J].

Loday, JL ;

Pirashvili, T .

JOURNAL OF ALGEBRA, 1996, 181 (02) :414-425

[10]

VERGNE M, 1970, B SOC MATH FR, V98, P81

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