Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras

被引：29
|
作者：
Adashev, J. K. [1 ]
Camacho, L. M. [2 ]
Omirov, B. A. [1 ]
机构：
[1] Natl Univ Uzbekistan, Inst Math, Tashkent 100125, Uzbekistan
[2] Univ Seville, Dept Matemat Aplicada 1, Avda Reina Mercedes S-N, E-41012 Seville, Spain
来源：
JOURNAL OF ALGEBRA | 2017年 / 479卷
关键词：
Leibniz algebra; Filiform algebra; Quasi-filiform algebra; Natural gradation; Characteristic sequence; 2-cocycles; Central extension;
D O I：
10.1016/j.jalgebra.2017.02.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we describe central extensions of some nilpotent Leibniz algebras. Namely, central extensions of the Leibniz algebra with maximal index of nilpotency are classified. Moreover, non-split central extensions of naturally graded filiform non-Lie Leibniz algebras are described up to isomorphism. It is shown that k-dimensional central extensions (k >= 5) of these algebras are split. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：461 / 486
页数：26
相关论文
共 50 条
  • [1] Solvable Leibniz algebras with naturally graded non-Lie p-filiform nilradicals
    Adashev, J. Q.
    Ladra, M.
    Omirov, B. A.
    COMMUNICATIONS IN ALGEBRA, 2017, 45 (10) : 4329 - 4347
  • [2] Non-associative central extensions of null-filiform associative algebras
    Kaygorodov, Ivan
    Lopes, Samuel A.
    Paez-Guillan, Pilar
    JOURNAL OF ALGEBRA, 2020, 560 : 1190 - 1210
  • [3] Classification of solvable Leibniz algebras with null-filiform nilradical
    Casas, J. M.
    Ladra, M.
    Omirov, B. A.
    Karimjanov, I. A.
    LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (06): : 758 - 774
  • [4] Extensions of solvable Lie algebras with naturally graded filiform nilradical
    Khudoyberdiyev, A. Kh.
    Sheraliyeva, S. A.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024, 23 (10)
  • [5] Abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras
    Jesus Calderon, Antonio
    Maria Camacho, Luisa
    Kaygorodov, Ivan
    Omirov, Bakhrom
    JOURNAL OF GEOMETRY AND PHYSICS, 2021, 170
  • [6] Solvable extensions of the naturally graded quasi-filiform Leibniz algebras
    Abdurasulov, K. K.
    Adashev, J. Q.
    COMMUNICATIONS IN ALGEBRA, 2023, 51 (02) : 510 - 527
  • [7] Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras
    Centrone, Lucio
    Zargeh, Chia
    ALGEBRAS AND REPRESENTATION THEORY, 2023, 26 (02) : 631 - 648
  • [8] Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras
    Lucio Centrone
    Chia Zargeh
    Algebras and Representation Theory, 2023, 26 : 631 - 648
  • [9] Polynomial identities and images of polynomials on null-filiform Leibniz algebras
    de Mello, Thiago Castilho
    Souza, Manuela da Silva
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2023, 679 : 246 - 260
  • [10] Local Derivations and Automorphisms of Direct Sum Null-Filiform Leibniz Algebras
    J. Q. Adashev
    B. B. Yusupov
    Lobachevskii Journal of Mathematics, 2022, 43 : 3407 - 3413
12345