Complete Leibniz algebras

被引：9
作者：
Boyle, Kristen [1 ]
Misra, Kailash C. [2 ]
Stitzinger, Ernest [2 ]
机构：
[1] Longwood Univ, Dept Math & Comp Sci, Farmville, VA 23909 USA
[2] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
来源：
JOURNAL OF ALGEBRA | 2020年 / 557卷
关键词：
Leibniz algebra; Derivations; Characteristic ideals; Completeness; IDEALS;
D O I：
10.1016/j.jalgebra.2020.04.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Leibniz algebras are certain generalizations of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of complete Leibniz algebras as a generalization of complete Lie algebras. Then we study properties of complete Leibniz algebras and their holomorphs. (C) 2020 Elsevier Inc. All rights reserved.
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收藏
页码：172 / 180
页数：9
相关论文
共 15 条
  • [1] Solvable Leibniz algebras with naturally graded non-Lie p-filiform nilradicals whose maximal complemented space of its nilradical
    Adashev, J. Q.
    Camacho, L. M.
    Omirov, B. A.
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (08) : 1500 - 1520
  • [2] [Anonymous], 1979, LIE ALGEBRAS
  • [3] Ayupov SA, 1998, ALGEBRA AND OPERATOR THEORY, P1
  • [4] Semisimple Leibniz algebras, their derivations and automorphisms
    Ayupov, Shavkat
    Kudaybergenov, Karimbergen
    Omirov, Bakhrom
    Zhao, Kaiming
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (10) : 2005 - 2019
  • [5] SOME THEOREMS ON LEIBNIZ ALGEBRAS
    Barnes, Donald W.
    [J]. COMMUNICATIONS IN ALGEBRA, 2011, 39 (07) : 2463 - 2472
  • [6] Bloch A., 1965, Math. in USSR Doklady, V165, P471
  • [7] Boyle K., 2018, THESIS
  • [8] Demir I., 2014, Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics Contemporary Mathematics, V623, P41
  • [9] Some remarks on semisimple Leibniz algebras
    Gomez-Vidal, S.
    Khudoyberdiyev, A. Kh.
    Omirov, B. A.
    [J]. JOURNAL OF ALGEBRA, 2014, 410 : 526 - 540
  • [10] Jacobson N., 1955, P AM MATH SOC, V6, P281, DOI 10.1090/S0002-9939-1955-0068532-9
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