The second cohomology group of simple Leibniz algebras

J. Q. Adashev; M. Ladra; B. A. Omirov

doi:10.1142/S0219498818502225

The second cohomology group of simple Leibniz algebras

J. Q. Adashev^*
, M. Ladra
, B. A. Omirov

^*Corresponding author for this work

National University of Uzbekistan named after Mirzo Ulugbek
University of Santiago de Compostela

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

2 Scopus citations

Abstract

In this paper, we prove some general results on Leibniz 2-cocyles for simple Leibniz algebras. Applying these results, we prove the triviality of the second Leibniz cohomology for a simple Leibniz algebra with coefficients in itself, whose associated Lie algebra is isomorphic to sl2.

Original language	English
Article number	1850222
Journal	Journal of Algebra and its Applications
Volume	17
Issue number	12
DOIs	https://doi.org/10.1142/S0219498818502225
State	Published - 1 Dec 2018
Externally published	Yes

Keywords

Leibniz algebra
Lie algebra
derivation
gradation
irreducible module
simple algebra
the second group of cohomology

Access to Document

10.1142/S0219498818502225

Cite this

@article{9a8383d108c64daeaf15c86666704185,

title = "The second cohomology group of simple Leibniz algebras",

abstract = "In this paper, we prove some general results on Leibniz 2-cocyles for simple Leibniz algebras. Applying these results, we prove the triviality of the second Leibniz cohomology for a simple Leibniz algebra with coefficients in itself, whose associated Lie algebra is isomorphic to sl2.",

keywords = "Leibniz algebra, Lie algebra, derivation, gradation, irreducible module, simple algebra, the second group of cohomology",

author = "Adashev, \{J. Q.\} and M. Ladra and Omirov, \{B. A.\}",

note = "Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",

year = "2018",

month = dec,

day = "1",

doi = "10.1142/S0219498818502225",

language = "英语",

volume = "17",

journal = "Journal of Algebra and its Applications",

issn = "0219-4988",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "12",

}

TY - JOUR

T1 - The second cohomology group of simple Leibniz algebras

AU - Adashev, J. Q.

AU - Ladra, M.

AU - Omirov, B. A.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - In this paper, we prove some general results on Leibniz 2-cocyles for simple Leibniz algebras. Applying these results, we prove the triviality of the second Leibniz cohomology for a simple Leibniz algebra with coefficients in itself, whose associated Lie algebra is isomorphic to sl2.

AB - In this paper, we prove some general results on Leibniz 2-cocyles for simple Leibniz algebras. Applying these results, we prove the triviality of the second Leibniz cohomology for a simple Leibniz algebra with coefficients in itself, whose associated Lie algebra is isomorphic to sl2.

KW - Leibniz algebra

KW - Lie algebra

KW - derivation

KW - gradation

KW - irreducible module

KW - simple algebra

KW - the second group of cohomology

UR - https://www.scopus.com/pages/publications/85043307622

U2 - 10.1142/S0219498818502225

DO - 10.1142/S0219498818502225

M3 - 文章

AN - SCOPUS:85043307622

SN - 0219-4988

VL - 17

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 12

M1 - 1850222

ER -

The second cohomology group of simple Leibniz algebras

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this