On description of Leibniz algebras corresponding to sl2

B. A. Omirov; I. S. Rakhimov; R. M. Turdibaev

doi:10.1007/s10468-012-9367-x

On description of Leibniz algebras corresponding to sl₂

B. A. Omirov
, I. S. Rakhimov^*
, R. M. Turdibaev

^*Corresponding author for this work

Academy of Sciences of the Republic of Uzbekistan
Universiti Putra Malaysia
National University of Uzbekistan named after Mirzo Ulugbek

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

29 Scopus citations

Abstract

In this paper we describe finite-dimensional complex Leibniz algebras whose quotient algebra with respect to the ideal I generated by squares is isomorphic to the simple Lie algebra sl ₂. It is shown that the number of isomorphism classes such of Leibniz algebras coincides with the number of partitions of dim I.

Original language	English
Pages (from-to)	1507-1519
Number of pages	13
Journal	Algebras and Representation Theory
Volume	16
Issue number	5
DOIs	https://doi.org/10.1007/s10468-012-9367-x
State	Published - Oct 2013
Externally published	Yes

Keywords

Irreducible module
Leibniz algebra
Lie algebra
Simple Leibniz algebra

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10.1007/s10468-012-9367-x

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title = "On description of Leibniz algebras corresponding to sl2",

abstract = "In this paper we describe finite-dimensional complex Leibniz algebras whose quotient algebra with respect to the ideal I generated by squares is isomorphic to the simple Lie algebra sl 2. It is shown that the number of isomorphism classes such of Leibniz algebras coincides with the number of partitions of dim I.",

keywords = "Irreducible module, Leibniz algebra, Lie algebra, Simple Leibniz algebra",

author = "Omirov, \{B. A.\} and Rakhimov, \{I. S.\} and Turdibaev, \{R. M.\}",

year = "2013",

month = oct,

doi = "10.1007/s10468-012-9367-x",

language = "英语",

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T1 - On description of Leibniz algebras corresponding to sl2

AU - Omirov, B. A.

AU - Rakhimov, I. S.

AU - Turdibaev, R. M.

PY - 2013/10

Y1 - 2013/10

N2 - In this paper we describe finite-dimensional complex Leibniz algebras whose quotient algebra with respect to the ideal I generated by squares is isomorphic to the simple Lie algebra sl 2. It is shown that the number of isomorphism classes such of Leibniz algebras coincides with the number of partitions of dim I.

AB - In this paper we describe finite-dimensional complex Leibniz algebras whose quotient algebra with respect to the ideal I generated by squares is isomorphic to the simple Lie algebra sl 2. It is shown that the number of isomorphism classes such of Leibniz algebras coincides with the number of partitions of dim I.

KW - Irreducible module

KW - Leibniz algebra

KW - Lie algebra

KW - Simple Leibniz algebra

UR - https://www.scopus.com/pages/publications/84885421237

U2 - 10.1007/s10468-012-9367-x

DO - 10.1007/s10468-012-9367-x

M3 - 文章

AN - SCOPUS:84885421237

SN - 1386-923X

VL - 16

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EP - 1519

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 5

ER -

On description of Leibniz algebras corresponding to sl₂

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Keywords

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