On the classification of complex leibniz superalgebras with characteristic sequence (n - 1, 1 m1,..., mk) and nilindex n + m

S. Albeverio; B. A. Omirov; A. K.H. Khodoyberdiyev

doi:10.1142/S0219498809003448

On the classification of complex leibniz superalgebras with characteristic sequence (n - 1, 1 m₁,..., m_k) and nilindex n + m

S. Albeverio^*
, B. A. Omirov
, A. K.H. Khodoyberdiyev

^*Corresponding author for this work

University of Bonn
Academy of Sciences of the Republic of Uzbekistan

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

6 Scopus citations

Abstract

In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n - 1, 1 m₁,..., m_k) and with nilindex equal to n + m. We prove that such superalgebras with the condition m₂ ≠ 0 have nilindex less than n + m. Therefore the complete classification of Leibniz algebras with characteristic sequence (n - 1, 1 m₁,..., m_k) and with nilindex equal to n + m is reduced to the classification of filiform Leibniz superalgebras of nilindex equal to n + m, which was provided in [3, 7].

Original language	English
Pages (from-to)	461-475
Number of pages	15
Journal	Journal of Algebra and its Applications
Volume	8
Issue number	4
DOIs	https://doi.org/10.1142/S0219498809003448
State	Published - 2009
Externally published	Yes

Keywords

Characteristic sequence
Leibniz superalgebras
Lie superalgebras
Nilpotency

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title = "On the classification of complex leibniz superalgebras with characteristic sequence (n - 1, 1 m1,..., mk) and nilindex n + m",

abstract = "In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n - 1, 1 m1,..., mk) and with nilindex equal to n + m. We prove that such superalgebras with the condition m2 ≠ 0 have nilindex less than n + m. Therefore the complete classification of Leibniz algebras with characteristic sequence (n - 1, 1 m1,..., mk) and with nilindex equal to n + m is reduced to the classification of filiform Leibniz superalgebras of nilindex equal to n + m, which was provided in [3, 7].",

keywords = "Characteristic sequence, Leibniz superalgebras, Lie superalgebras, Nilpotency",

author = "S. Albeverio and Omirov, \{B. A.\} and Khodoyberdiyev, \{A. K.H.\}",

year = "2009",

doi = "10.1142/S0219498809003448",

language = "英语",

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pages = "461--475",

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T1 - On the classification of complex leibniz superalgebras with characteristic sequence (n - 1, 1 m1,..., mk) and nilindex n + m

AU - Albeverio, S.

AU - Omirov, B. A.

AU - Khodoyberdiyev, A. K.H.

PY - 2009

Y1 - 2009

N2 - In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n - 1, 1 m1,..., mk) and with nilindex equal to n + m. We prove that such superalgebras with the condition m2 ≠ 0 have nilindex less than n + m. Therefore the complete classification of Leibniz algebras with characteristic sequence (n - 1, 1 m1,..., mk) and with nilindex equal to n + m is reduced to the classification of filiform Leibniz superalgebras of nilindex equal to n + m, which was provided in [3, 7].

AB - In this work we investigate the complex Leibniz superalgebras with characteristic sequence (n - 1, 1 m1,..., mk) and with nilindex equal to n + m. We prove that such superalgebras with the condition m2 ≠ 0 have nilindex less than n + m. Therefore the complete classification of Leibniz algebras with characteristic sequence (n - 1, 1 m1,..., mk) and with nilindex equal to n + m is reduced to the classification of filiform Leibniz superalgebras of nilindex equal to n + m, which was provided in [3, 7].

KW - Characteristic sequence

KW - Leibniz superalgebras

KW - Lie superalgebras

KW - Nilpotency

UR - https://www.scopus.com/pages/publications/70349470689

U2 - 10.1142/S0219498809003448

DO - 10.1142/S0219498809003448

M3 - 文章

AN - SCOPUS:70349470689

SN - 0219-4988

VL - 8

SP - 461

EP - 475

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 4

ER -

On the classification of complex leibniz superalgebras with characteristic sequence (n - 1, 1 m₁,..., m_k) and nilindex n + m

Abstract

Keywords

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