On Derivations of Semisimple Leibniz Algebras

I. S. Rakhimov; K. K. Masutova; B. A. Omirov

doi:10.1007/s40840-015-0113-5

On Derivations of Semisimple Leibniz Algebras

I. S. Rakhimov^*
, K. K. Masutova
, B. A. Omirov

^*Corresponding author for this work

Universiti Putra Malaysia
National University of Uzbekistan named after Mirzo Ulugbek

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In the paper, we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are Lie algebra derivations and the third one can be explicitly described. Then we show that the similar description can be found as well as for a subclass of semisimple Leibniz algebras.

Original language	English
Pages (from-to)	295-306
Number of pages	12
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	40
Issue number	1
DOIs	https://doi.org/10.1007/s40840-015-0113-5
State	Published - 1 Jan 2017
Externally published	Yes

Keywords

Derivation
Inner derivation
Irreducible module
Leibniz algebra
Lie algebra
Semisimple algebra
Simple algebra

Access to Document

10.1007/s40840-015-0113-5

Cite this

@article{c72618c96c634caba16208890ef1addd,

title = "On Derivations of Semisimple Leibniz Algebras",

abstract = "In the paper, we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are Lie algebra derivations and the third one can be explicitly described. Then we show that the similar description can be found as well as for a subclass of semisimple Leibniz algebras.",

keywords = "Derivation, Inner derivation, Irreducible module, Leibniz algebra, Lie algebra, Semisimple algebra, Simple algebra",

author = "Rakhimov, \{I. S.\} and Masutova, \{K. K.\} and Omirov, \{B. A.\}",

note = "Publisher Copyright: {\textcopyright} 2015, Malaysian Mathematical Sciences Society and Universiti Sains Malaysia.",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/s40840-015-0113-5",

language = "英语",

volume = "40",

pages = "295--306",

journal = "Bulletin of the Malaysian Mathematical Sciences Society",

issn = "0126-6705",

publisher = "Springer Singapore",

number = "1",

}

TY - JOUR

T1 - On Derivations of Semisimple Leibniz Algebras

AU - Rakhimov, I. S.

AU - Masutova, K. K.

AU - Omirov, B. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In the paper, we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are Lie algebra derivations and the third one can be explicitly described. Then we show that the similar description can be found as well as for a subclass of semisimple Leibniz algebras.

AB - In the paper, we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are Lie algebra derivations and the third one can be explicitly described. Then we show that the similar description can be found as well as for a subclass of semisimple Leibniz algebras.

KW - Derivation

KW - Inner derivation

KW - Irreducible module

KW - Leibniz algebra

KW - Lie algebra

KW - Semisimple algebra

KW - Simple algebra

UR - https://www.scopus.com/pages/publications/85008613710

U2 - 10.1007/s40840-015-0113-5

DO - 10.1007/s40840-015-0113-5

M3 - 文章

AN - SCOPUS:85008613710

SN - 0126-6705

VL - 40

SP - 295

EP - 306

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 1

ER -

On Derivations of Semisimple Leibniz Algebras

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this