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Sibirsk. Mat. Zh., 2011, Volume 52, Number 5, Pages 1058–1073 (Mi smj2258)  

This article is cited in 5 scientific papers (total in 5 papers)

Quasi-filiform Leibniz algebras of maximum length

L. M. Camachoa, E. M. Cañetea, J. R. Gómeza, B. A. Omirovb

a University of Seville, Seville, Spain
b Institute of Mathematics and Information Technologies, Tashkent, Uzbekistan

Abstract: The $n$-dimensional $p$-filiform Leibniz algebras of maximum length have already been studied with $0\le p\le2$. For Lie algebras whose nilindex is equal to $n-2$ there is only one characteristic sequence, $(n-2,1,1)$, while in Leibniz theory we obtain the two possibilities: $(n-2,1,1)$ and $(n-2,2)$. The first case (the $2$-filiform case) is already known. The present paper deals with the second case, i.e., quasi-filiform non-Lie-Leibniz algebras of maximum length. Therefore this work completes the study of the maximum length of the Leibniz algebras with nilindex $n-p$ with $0\le p\le2$.

Keywords: Lie algebra, Leibniz algebra, nilpotence, natural gradation, characteristic sequence, $p$-filiformness.

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English version:
Siberian Mathematical Journal, 2011, 52:5, 840–853

Bibliographic databases:

UDC: 512.554.38
Received: 25.11.2009
Revised: 04.03.2011

Citation: L. M. Camacho, E. M. Cañete, J. R. Gómez, B. A. Omirov, “Quasi-filiform Leibniz algebras of maximum length”, Sibirsk. Mat. Zh., 52:5 (2011), 1058–1073; Siberian Math. J., 52:5 (2011), 840–853

Citation in format AMSBIB
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\by L.~M.~Camacho, E.~M.~Ca{\~n}ete, J.~R.~G\'omez, B.~A.~Omirov
\paper Quasi-filiform Leibniz algebras of maximum length
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 5
\pages 1058--1073
\mathnet{http://mi.mathnet.ru/smj2258}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2908127}
\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 5
\pages 840--853
\crossref{https://doi.org/10.1134/S0037446611050090}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80155177843}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Camacho L.M. Canete E.M. Gomez J.R. Omirov B.A., “P-Filiform Leibniz Algebras of Maximum Length”, Linear Alg. Appl., 450 (2014), 316–333  crossref  mathscinet  zmath  isi  elib  scopus
    2. L. M. Camacho, E. M. Cañete, J. R. Gómez, B. A. Omirov, “$3$-filiform Leibniz algebras of maximum length”, Siberian Math. J., 57:1 (2016), 24–35  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. Shabanskaya, “Solvable extensions of naturally graded quasi-filiform Leibniz algebras of second type l-1 and l-3”, Commun. Algebr., 45:10 (2017), 4492–4520  crossref  mathscinet  zmath  isi  scopus
    4. A. Shabanskaya, “Right and left solvable extensions of an associative Leibniz algebra”, Commun. Algebr., 45:6 (2017), 2633–2661  crossref  mathscinet  zmath  isi  scopus
    5. Shabanskaya A., “Solvable Extensions of the Naturally Graded Quasi-Filiform Leibniz Algebra of Second Type l-2”, Commun. Algebr., 46:11 (2018), 5006–5031  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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