Special Issues

The algebraic classification of nilpotent commutative algebras

  • Received: 01 February 2021 Revised: 01 July 2021 Published: 07 September 2021
  • Primary: 17A01; Secondary: 17D99, 17A99

  • This paper is devoted to the complete algebraic classification of complex $ 5 $-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller nilpotent commutative algebras and the recently obtained classification of complex $ 5 $-dimensional nilpotent commutative $ \mathfrak{CD} $-algebras.

    Citation: Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev. The algebraic classification of nilpotent commutative algebras[J]. Electronic Research Archive, 2021, 29(6): 3909-3993. doi: 10.3934/era.2021068

    Related Papers:

  • This paper is devoted to the complete algebraic classification of complex $ 5 $-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller nilpotent commutative algebras and the recently obtained classification of complex $ 5 $-dimensional nilpotent commutative $ \mathfrak{CD} $-algebras.



    加载中


    [1] Classification of three-dimensional evolution algebras. Linear Algebra Appl. (2017) 524: 68-108.
    [2] The classification of $4$-dimensional Leibniz algebras. Linear Algebra Appl. (2013) 439: 273-288.
    [3] Six-dimensional nilpotent Lie algebras. Linear Algebra Appl. (2012) 436: 163-189.
    [4] The classification of 5-dimensional $p$-nilpotent restricted Lie algebras over perfect fields, I.. J. Algebra (2016) 464: 97-140.
    [5] Classification of the four-dimensional power-commutative real division algebras. Proc. Roy. Soc. Edinburgh Sect. A (2011) 141: 1207-1223.
    [6] Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not $2$. J. Algebra (2007) 309: 640-653.
    [7] On the classification of $4$-dimensional quadratic division algebras over square-ordered fields. J. London Math. Soc. (2) (2002) 65: 285-302.
    [8] A. Fernández Ouaridi, I. Kaygorodov, M. Khrypchenko and Yu. Volkov, Degenerations of nilpotent algebras, J. Pure Appl. Algebra, 226 (2022), Paper No. 106850, 21 pp. doi: 10.1016/j.jpaa.2021.106850
    [9] Classification of five-dimensional nilpotent Jordan algebras. Linear Algebra Appl. (2016) 494: 165-218.
    [10] The classification of $n$-dimensional non-Lie Malcev algebras with $(n-4)$-dimensional annihilator. Linear Algebra Appl. (2016) 505: 32-56.
    [11] D. Jumaniyozov, I. Kaygorodov and A. Khudoyberdiyev, The algebraic classification of nilpotent commutative $\mathfrak {CD}$-algebras, Communications in Algebra, 49 (2021), 1464–1494. doi: 10.1080/00927872.2020.1837852
    [12] I. Kaygorodov, M. Khrypchenko and S. A. Lopes, The algebraic and geometric classification of nilpotent anticommutative algebras, Journal of Pure and Applied Algebra, 224 (2020), 106337, 32 pp. doi: 10.1016/j.jpaa.2020.106337
    [13] I. Kaygorodov, M. Khrypchenko and S. Lopes, The algebraic classification of nilpotent algebras, arXiv: 2012.00525.
    [14] I. Kaygorodov, M. Khrypchenko and Yu. Popov, The algebraic and geometric classification of nilpotent terminal algebras, J. Pure Appl. Algebra, 225 (2021), 106625, 41 pp. doi: 10.1016/j.jpaa.2020.106625
    [15] I. Kaygorodov, I. Rakhimov and Sh. K. Said Husain, The algebraic classification of nilpotent associative commutative algebras, J. Algebra Appl., 19 (2020), 2050220, 14 pp. doi: 10.1142/S0219498820502205
    [16] The variety of $2$-dimensional algebras over an algebraically closed field. Canad. J. Math. (2019) 71: 819-842.
    [17] Classification of three-dimensional zeropotent algebras over an algebraically closed field. Comm. Algebra (2017) 45: 5037-5052.
    [18] Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. (1980) 55: 267-293.
    [19] The classification of two-dimensional nonassociative algebras. Results Math. (2000) 37: 120-154.
    [20] T. Skjelbred and T. Sund, Sur la classification des algebres de Lie nilpotentes, C. R. Acad. Sci. Paris Sér. A-B, 286 (1978), A241–A242.
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(654) PDF downloads(103) Cited by(0)

Article outline

Figures and Tables

Tables(3)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog