Leibniz algebras constructed by Witt algebras

被引：1

作者：

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

Omirov, B. A. ^{[2
]}

Kurbanbaev, T. K. ^{[3
]}

机构：

[1] Univ Seville, Dpto Matemat Aplicada 1, Avda Reina Mercedes, E-41012 Seville, Spain

[2] Natl Univ Uzbekistan, Dept Algebra & Funct Anal, Tashkent, Uzbekistan

[3] Uzbek Acad Sci, Inst Math, Tashkent, Uzbekistan

来源：

LINEAR & MULTILINEAR ALGEBRA | 2019年 / 67卷 / 10期

关键词：

Leibniz algebra; Witt Lie algebra; Leibniz representation; right Lie module; classification; REPRESENTATIONS; MODULES;

D O I：

10.1080/03081087.2018.1480704

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself.

引用

页码：2048 / 2064

页数：17

共 24 条

[1]

Adashev JQ, 2016, 160704949 ARXIV

[2] On nilpotent and simple Leibniz algebras [J].

Albeverio, S ;

Ayupov, SA ;

Omirov, BA .

COMMUNICATIONS IN ALGEBRA, 2005, 33 (01) :159-172

[3]

Albeverio SA., 2006, Rev. Mat. Complut, V19, P183

[4]

Ayupov SA, ARXIV170808082V1

[5] Leibniz algebras associated with representations of filiform Lie algebras [J].

Ayupov, Sh. A. ;

Camacho, L. M. ;

Khudoyberdiyev, A. Kh. ;

Omirov, B. A. .

JOURNAL OF GEOMETRY AND PHYSICS, 2015, 98 :181-195

[6]

Ayupov ShA, 1998, LEIBNIZ ALGEBRAS ALG, P1

[7] ON LEVI'S THEOREM FOR LEIBNIZ ALGEBRAS [J].

Barnes, Donald W. .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2012, 86 (02) :184-185

[8] ON ENGEL'S THEOREM FOR LEIBNIZ ALGEBRAS [J].

Barnes, Donald W. .

COMMUNICATIONS IN ALGEBRA, 2012, 40 (04) :1388-1389

[9]

Bosko L., 2011, Involve, V4, P293, DOI DOI 10.2140/INVOLVE.2011.4.293

[10] Leibniz algebras of Heisenberg type [J].

Calderon, A. J. ;

Camacho, L. M. ;

Omirov, B. A. .

JOURNAL OF ALGEBRA, 2016, 452 :427-447

← 1 2 3 →