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

K.K. Abdurasulov; A.Kh. Khudoyberdiyev; M. Ladra; A.M. Sattarov

Communications in Mathematics (2021)

  • Volume: 29, Issue: 2, page 187-213
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Abdurasulov, K.K., et al. "Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras." Communications in Mathematics 29.2 (2021): 187-213. <http://eudml.org/doc/297473>.

@article{Abdurasulov2021,
abstract = {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.},
author = {Abdurasulov, K.K., Khudoyberdiyev, A.Kh., Ladra, M., Sattarov, A.M.},
journal = {Communications in Mathematics},
keywords = {Lie algebra; Leibniz algebra; derivation; pre-derivation; nilpotency; characteristically nilpotent algebra; strongly nilpotent algebra},
language = {eng},
number = {2},
pages = {187-213},
publisher = {University of Ostrava},
title = {Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras},
url = {http://eudml.org/doc/297473},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Abdurasulov, K.K.
AU - Khudoyberdiyev, A.Kh.
AU - Ladra, M.
AU - Sattarov, A.M.
TI - Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 2
SP - 187
EP - 213
AB - 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.
LA - eng
KW - Lie algebra; Leibniz algebra; derivation; pre-derivation; nilpotency; characteristically nilpotent algebra; strongly nilpotent algebra
UR - http://eudml.org/doc/297473
ER -

References

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