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 50 条

[1] Leibniz Algebras Constructed by Representations of General Diamond Lie Algebras
Camacho, L. M.
Karimjanov, I. A.
Ladra, M.
Omirov, B. A.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (03) : 1281 - 1293
[2] Leibniz Algebras Constructed by Representations of General Diamond Lie Algebras
L. M. Camacho
I. A. Karimjanov
M. Ladra
B. A. Omirov
Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42 : 1281 - 1293
[3] Poincare'-Birkhoff-Witt theorem for Leibniz n-algebras
Casas, Jose Manuel
Insua, Manuel A.
Ladra, Manuel
JOURNAL OF SYMBOLIC COMPUTATION, 2007, 42 (11-12) : 1052 - 1065
[4] Leibniz Algebras and Lie Algebras
Mason, Geoffrey
Yamskulna, Caywalee
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2013, 9
[5] On Leibniz algebras
Ayupov, SA
Omirov, BA
ALGEBRA AND OPERATOR THEORY, 1998, : 1 - 12
[6] REPRESENTATIONS OF WITT ALGEBRAS
RAO, SE
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1994, 30 (02) : 191 - 201
[7] Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras
Stitzinger, Ernie
White, Ashley
ALGEBRAS AND REPRESENTATION THEORY, 2018, 21 (03) : 627 - 633
[8] Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras
Ernie Stitzinger
Ashley White
Algebras and Representation Theory, 2018, 21 : 627 - 633
[9] Leibniz algebras as non-associative algebras
Feldvoss, Jorg
NONASSOCIATIVE MATHEMATICS AND ITS APPLICATIONS, 2019, 721 : 115 - 149
[10] On the representability of actions of Leibniz algebras and Poisson algebras
Cigoli, Alan S.
Mancini, Manuel
Metere, Giuseppe
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2023, 66 (04) : 998 - 1021

← 1 2 3 4 5 →