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J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 2, Pages 173–184 (Mi jsfu747)  

This article is cited in 11 scientific papers (total in 11 papers)

The variety of nilpotent Tortkara algebras

Ilya B. Gorshkova, Ivan Kaygorodovb, Alexey A. Kytmanovc, Mohamed A. Salimd

a Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
b CMCC, Universidade Federal do ABC, Santo André, Brasil
c Institute of Space and Information Technologies, Siberian Federal University, Kirensky, 26, Krasnoyarsk, 660074, Russia
d United Arab Emirates University, Al Ain, UAE

Abstract: We give algebraic and geometric classification of all $5$-dimensional nilpotent Tortkara algebras over complex field.

Keywords: Tortkara algebra, algeraic classification, central extension, geometric classification, degenerations.

Funding Agency Grant Number
Russian Science Foundation 18-71-10007
United Arab Emirates University (9) 2017 Grant G00002599
The first part of this work is supported by the Russian Science Foundation under grant 18-71-10007. The second part of this work was supported by UAEU UPAR (9) 2017 Grant G00002599 (Mohamed A. Salim).


DOI: https://doi.org/10.17516/1997-1397-2019-12-2-173-184

Full text: PDF file (209 kB)
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Bibliographic databases:

UDC: 512.554.1
Received: 06.11.2018
Received in revised form: 06.12.2018
Accepted: 06.08.2018
Language:

Citation: Ilya B. Gorshkov, Ivan Kaygorodov, Alexey A. Kytmanov, Mohamed A. Salim, “The variety of nilpotent Tortkara algebras”, J. Sib. Fed. Univ. Math. Phys., 12:2 (2019), 173–184

Citation in format AMSBIB
\Bibitem{GorKayKyt19}
\by Ilya~B.~Gorshkov, Ivan~Kaygorodov, Alexey~A.~Kytmanov, Mohamed~A.~Salim
\paper The variety of nilpotent Tortkara algebras
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 2
\pages 173--184
\mathnet{http://mi.mathnet.ru/jsfu747}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-2-173-184}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000467247000004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alvarez M.A., “Degenerations of 8-Dimensional 2-Step Nilpotent Lie Algebras”, Algebr. Represent. Theory  crossref  mathscinet  isi  scopus
    2. Camacho L.M., Karimjanov I., Kaygorodov I., Khudoyberdiyev A., “Central Extensions of Filiform Zinbiel Algebras”, Linear Multilinear Algebra  crossref  mathscinet  isi  scopus
    3. Camacho L.M., Karimjanov I., Kaygorodov I., Khudoyberdiyev A., “One-Generated Nilpotent Novikov Algebras”, Linear Multilinear Algebra  crossref  isi  scopus
    4. Karimjanov I., Kaygorodov I., Khudoyberdiyev A., “the Algebraic and Geometric Classification of Nilpotent Novikov Algebras”, J. Geom. Phys., 143 (2019), 11–21  crossref  mathscinet  zmath  isi  scopus
    5. I. Kaygorodov, S. A. Lopes, Yu. Popov, “Degenerations of nilpotent associative commutative algebras”, Commun. Algebr., 48:4 (2020), 1632–1639  crossref  mathscinet  zmath  isi  scopus
    6. I. Gorshkov, I. Kaygorodov, M. Khrypchenko, “The geometric classification of nilpotent tortkara algebras”, Commun. Algebr., 48:1 (2020), 204–209  crossref  zmath  isi  scopus
    7. I. Kaygorodov, I. Rakhimov, Sh. K. S. Husain, “The algebraic classification of nilpotent associative commutative algebras”, J. Algebra. Appl., 19:11 (2020), 2050220  crossref  mathscinet  zmath  isi  scopus
    8. I. Kaygorodov, M. Khrypchenko, S. A. Lopes, “The algebraic and geometric classification of nilpotent anticommutative algebras”, J. Pure Appl. Algebr., 224:8 (2020), 106337  crossref  mathscinet  zmath  isi  scopus
    9. I. Gorshkov, I. Kaygorodov, M. Khrypchenko, “The algebraic classification of nilpotent tortkara algebras”, Commun. Algebr., 48:8 (2020), 3608–3623  crossref  mathscinet  zmath  isi  scopus
    10. I. Kaygorodov, P. Paez-Guillan, V. Voronin, “The algebraic and geometric classification of nilpotent bicommutative algebras”, Algebr. Represent. Theory, 23:6 (2020), 2331–2347  crossref  mathscinet  zmath  isi  scopus
    11. Ismailov N., Kaygorodov I., Mashurov F., “the Algebraic and Geometric Classification of Nilpotent Assosymmetric Algebras”, Algebr. Represent. Theory, 24:1 (2021), 135–148  crossref  mathscinet  isi  scopus
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