Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We de...

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Main Authors:	Abdurasulov K.K., Khudoyberdiyev A. Kh., Ladra M., Sattarov A.M.
Format:	Article
Language:	English
Published:	Sciendo 2021-06-01
Series:	Communications in Mathematics
Subjects:	lie algebra leibniz algebra derivation pre-derivation nilpotency characteristically nilpotent algebra strongly nilpotent algebra 17a32 17a36 17b30
Online Access:	https://doi.org/10.2478/cm-2021-0018

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spelling	doaj-6e009d2de7ae4b29b8c8e31a04c1b18b2021-09-06T19:22:06ZengSciendoCommunications in Mathematics2336-12982021-06-0129218721310.2478/cm-2021-0018Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebrasAbdurasulov K.K.0Khudoyberdiyev A. Kh.1Ladra M.2Sattarov A.M.3V.I. Romanovsky Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, 100174, UzbekistanNational University of Uzbekistan, Tashkent, 100174, V.I. Romanovsky Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, 100174, UzbekistanDepartment of Mathematics, Institute of Mathematics, Campus Vida, University of Santiago de Compostela, 15782, SpainV.I. Romanovsky Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, 100174, UzbekistanIn this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.https://doi.org/10.2478/cm-2021-0018lie algebraleibniz algebraderivationpre-derivationnilpotencycharacteristically nilpotent algebrastrongly nilpotent algebra17a3217a3617b30
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Abdurasulov K.K. Khudoyberdiyev A. Kh. Ladra M. Sattarov A.M.
spellingShingle	Abdurasulov K.K. Khudoyberdiyev A. Kh. Ladra M. Sattarov A.M. Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras Communications in Mathematics lie algebra leibniz algebra derivation pre-derivation nilpotency characteristically nilpotent algebra strongly nilpotent algebra 17a32 17a36 17b30
author_facet	Abdurasulov K.K. Khudoyberdiyev A. Kh. Ladra M. Sattarov A.M.
author_sort	Abdurasulov K.K.
title	Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
title_short	Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
title_full	Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
title_fullStr	Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
title_full_unstemmed	Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
title_sort	pre-derivations and description of non-strongly nilpotent filiform leibniz algebras
publisher	Sciendo
series	Communications in Mathematics
issn	2336-1298
publishDate	2021-06-01
description	In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.
topic	lie algebra leibniz algebra derivation pre-derivation nilpotency characteristically nilpotent algebra strongly nilpotent algebra 17a32 17a36 17b30
url	https://doi.org/10.2478/cm-2021-0018
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Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

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