On derivations of Leibniz algebras

被引：0

作者：

Misra, Kailash C. ^{[1
]}

Patlertsin, Sutida ^{[2
]}

Pongprasert, Suchada ^{[2
]}

Rungratgasame, Thitarie ^{[2
]}

机构：

[1] North Carolina State Univ, Dept Math, Raleigh, NC USA

[2] Srinakharinwirot Univ, Fac Sci, Dept Math, Bangkok, Thailand

来源：

ELECTRONIC RESEARCH ARCHIVE | 2024年 / 32卷 / 07期

关键词：

Leibniz algebra; completeness; extension; holomorph; derivation; direct sum; decomposition;

D O I：

10.3934/era.2024214

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Leibniz algebras are non-antisymmetric generalizations of Lie algebras. In this paper, we investigate the properties of complete Leibniz algebras under certain conditions on their extensions. Additionally, we explore the properties of derivations and direct sums of Leibniz algebras, proving several results analogous to those in Lie algebras.

引用

页码：4715 / 4722

页数：8

共 9 条

[1] On a complete rigid Leibniz non-Lie algebra in arbitrary dimension
Ancochea Bermudez, J. M.
Campoamor-Stursberg, R.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (08) : 3397 - 3407
[2] A note on outer derivations of Leibniz algebras
Biyogmam, G. R.
Tcheka, C.
[J]. COMMUNICATIONS IN ALGEBRA, 2021, 49 (05) : 2190 - 2198
[3] BLOKH A, 1965, DOKL AKAD NAUK SSSR+, V165, P471
[4] Complete Leibniz algebras
Boyle, Kristen
Misra, Kailash C.
Stitzinger, Ernest
[J]. JOURNAL OF ALGEBRA, 2020, 557 : 172 - 180
[5] Jacobson N., 1962, LIE ALGEBRAS
[6] Kongsomprach Y, 2024, THAI J MATH, V22, P165
[7] Loday J.-L., 1993, ENSEIGN MATH, V39, P269
[8] MENG DJ, 1994, COMMUN ALGEBRA, V22, P5457
[9] On Inner Derivations of Leibniz Algebras
Patlertsin, Sutida
Pongprasert, Suchada
Rungratgasame, Thitarie
[J]. MATHEMATICS, 2024, 12 (08)

← 1 →