Maximal Solvable Extension of Naturally Graded Filiform n-Lie Algebras

K. K. Abdurasulov; R. K. Gaybullaev; B. A. Omirov; A. Kh Khudoyberdiyev

doi:10.1134/S0037446622010013

Maximal Solvable Extension of Naturally Graded Filiform n-Lie Algebras

K. K. Abdurasulov^*
, R. K. Gaybullaev
, B. A. Omirov
, A. Kh Khudoyberdiyev

^*Corresponding author for this work

Romanovskii Institute of Mathematics
National University of Uzbekistan named after Mirzo Ulugbek

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

Abstract

We study naturally graded filiform $ n $-Lie algebras. Among these algebras,we distinguish some algebra with the simplest structurethat is an analog of the model filiform Lie algebra.We describe the derivations of the algebra and obtainthe classification of solvable $ n $-Lie algebraswhose maximal hyponilpotent ideal coincides with thedistinguished naturally graded filiform algebra. Furthermore,we show that these solvable $ n $-Lie algebras possessouter derivations.

Original language	English
Journal	Siberian Mathematical Journal
Volume	63
Issue number	1
DOIs	https://doi.org/10.1134/S0037446622010013
State	Published - Jan 2022
Externally published	Yes

Keywords

$ n $-Lie algebra
512.554
Filippov algebra
characteristic sequence
derivation
graded algebra
hyponilpotent ideal of an $ n $-algebra
nilpotent $ n $-algebra
solvable $ n $-algebra

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10.1134/S0037446622010013

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title = "Maximal Solvable Extension of Naturally Graded Filiform n-Lie Algebras",

abstract = "We study naturally graded filiform \$ n \$-Lie algebras. Among these algebras,we distinguish some algebra with the simplest structurethat is an analog of the model filiform Lie algebra.We describe the derivations of the algebra and obtainthe classification of solvable \$ n \$-Lie algebraswhose maximal hyponilpotent ideal coincides with thedistinguished naturally graded filiform algebra. Furthermore,we show that these solvable \$ n \$-Lie algebras possessouter derivations.",

keywords = "\$ n \$-Lie algebra, 512.554, Filippov algebra, characteristic sequence, derivation, graded algebra, hyponilpotent ideal of an \$ n \$-algebra, nilpotent \$ n \$-algebra, solvable \$ n \$-algebra",

author = "Abdurasulov, \{K. K.\} and Gaybullaev, \{R. K.\} and Omirov, \{B. A.\} and Khudoyberdiyev, \{A. Kh\}",

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year = "2022",

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doi = "10.1134/S0037446622010013",

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T1 - Maximal Solvable Extension of Naturally Graded Filiform n-Lie Algebras

AU - Abdurasulov, K. K.

AU - Gaybullaev, R. K.

AU - Omirov, B. A.

AU - Khudoyberdiyev, A. Kh

PY - 2022/1

Y1 - 2022/1

N2 - We study naturally graded filiform $ n $-Lie algebras. Among these algebras,we distinguish some algebra with the simplest structurethat is an analog of the model filiform Lie algebra.We describe the derivations of the algebra and obtainthe classification of solvable $ n $-Lie algebraswhose maximal hyponilpotent ideal coincides with thedistinguished naturally graded filiform algebra. Furthermore,we show that these solvable $ n $-Lie algebras possessouter derivations.

AB - We study naturally graded filiform $ n $-Lie algebras. Among these algebras,we distinguish some algebra with the simplest structurethat is an analog of the model filiform Lie algebra.We describe the derivations of the algebra and obtainthe classification of solvable $ n $-Lie algebraswhose maximal hyponilpotent ideal coincides with thedistinguished naturally graded filiform algebra. Furthermore,we show that these solvable $ n $-Lie algebras possessouter derivations.

KW - $ n $-Lie algebra

KW - 512.554

KW - Filippov algebra

KW - characteristic sequence

KW - derivation

KW - graded algebra

KW - hyponilpotent ideal of an $ n $-algebra

KW - nilpotent $ n $-algebra

KW - solvable $ n $-algebra

UR - https://www.scopus.com/pages/publications/85123953371

U2 - 10.1134/S0037446622010013

DO - 10.1134/S0037446622010013

M3 - 文章

AN - SCOPUS:85123953371

SN - 0037-4466

VL - 63

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

IS - 1

ER -

Maximal Solvable Extension of Naturally Graded Filiform n-Lie Algebras

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Keywords

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