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

[41] WITT RINGS OF QUATERNION ALGEBRAS
SLADEK, A
JOURNAL OF ALGEBRA, 1986, 103 (01) : 267 - 272
[42] Local derivations on Witt algebras
Chen, Yang
Zhao, Kaiming
Zhao, Yueqiang
LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (06): : 1159 - 1172
[43] Generalised Witt algebras and idealizers
Sierra, Susan J.
Spenko, Spela
JOURNAL OF ALGEBRA, 2017, 483 : 415 - 428
[44] Witt type Lie algebras
Yu, RWT
COMMUNICATIONS IN ALGEBRA, 1997, 25 (05) : 1471 - 1484
[45] Simple Deformed Witt Algebras
Song, Guang'ai
Xia, Chunguang
ALGEBRA COLLOQUIUM, 2011, 18 (03) : 533 - 540
[46] Grobner bases in universal enveloping algebras of Leibniz algebras
Insua, Manuel A.
Ladra, Manuel
JOURNAL OF SYMBOLIC COMPUTATION, 2009, 44 (05) : 517 - 526
[47] From Leibniz Algebras to Lie 2-algebras
Sheng, Yunhe
Liu, Zhangju
ALGEBRAS AND REPRESENTATION THEORY, 2016, 19 (01) : 1 - 5
[48] Leibniz algebras associated with representations of filiform Lie algebras
Ayupov, Sh. A.
Camacho, L. M.
Khudoyberdiyev, A. Kh.
Omirov, B. A.
JOURNAL OF GEOMETRY AND PHYSICS, 2015, 98 : 181 - 195
[49] From Leibniz Algebras to Lie 2-algebras
Yunhe Sheng
Zhangju Liu
Algebras and Representation Theory, 2016, 19 : 1 - 5
[50] JACOBSON-WITT ALGEBRAS AND LIE-ADMISSIBLE ALGEBRAS
TOMBER, ML
HADRONIC JOURNAL, 1981, 4 (02): : 183 - 198

← 1 2 3 4 5 →