Homology of multiplicative Lie rings

被引：18
|
作者：
Bak, A.
Donadze, G.
Inassaridze, N.
Ladra, M.
机构：
[1] Univ Bielefeld, Dept Math, D-33501 Bielefeld, Germany
[2] Georgian Acad Sci, A Razmadze Math Inst, GE-0193 Tbilisi, Georgia
[3] Univ Santiago de Compostela, Fac Matemat, Dept Algebra, Santiago De Compostela 15782, Spain
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2007年 / 208卷 / 02期
关键词：
D O I：
10.1016/j.jpaa.2006.03.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Two homology theories of multiplicative Lie rings are constructed, studied and compared with the usual homology theories of groups and Lie rings. Central extensions of multiplicative Lie rings are introduced. It is shown that the Steinberg multiplicative Lie ring of a ring is the direct product of the Steinberg group (viewed as a multiplicative Lie ring under the commutator bracket) and the Steinberg Lie ring. (c) 2006 Published by Elsevier B.V.
引用
收藏
页码：761 / 777
页数：17
相关论文
共 50 条
  • [1] Exact sequences in homology of multiplicative Lie rings and a new version of Stallings' theorem
    Donadze, G.
    Inassaridze, N.
    Ladra, M.
    Vieites, A. M.
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2018, 222 (07) : 1786 - 1802
  • [2] Homology of Free Nilpotent Lie Rings
    Romanovskii V.R.
    Journal of Mathematical Sciences, 2020, 247 (4) : 632 - 639
  • [3] Multiplicative Lie-Type Derivations on Rings
    Mohammad Ashraf
    Mohd Shuaib Akhtar
    Bilal Ahmad Wani
    Mohit Kumar
    Bulletin of the Iranian Mathematical Society, 2022, 48 : 1217 - 1227
  • [4] Multiplicative Lie-Type Derivations on Rings
    Ashraf, Mohammad
    Akhtar, Mohd Shuaib
    Wani, Bilal Ahmad
    Kumar, Mohit
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (04) : 1217 - 1227
  • [5] CHARACTERIZATION OF LIE MULTIPLICATIVE DERIVATION ON ALTERNATIVE RINGS
    Macedo Ferreira, Bruno Leonardo
    Guzzo Jr, Henrique
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2019, 49 (03) : 761 - 772
  • [6] Characterization of Multiplicative Lie Triple Derivations on Rings
    Qi, Xiaofei
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [7] Multiplicative lie isomorphisms between prime rings
    Bai, Zhaofang
    Du, Shuanping
    Hou, Jinchuan
    COMMUNICATIONS IN ALGEBRA, 2008, 36 (05) : 1626 - 1633
  • [8] HOMOLOGY THEORY OF MULTIPLICATIVE HOM-LIE ALGEBRAS
    Xu, Maosen
    Wu, Zhixiang
    MATHEMATICAL REPORTS, 2023, 25 (02): : 331 - 347
  • [9] On homology of Lie algebras over commutative rings
    Ivanov, Sergei O.
    Pavutnitskiy, Fedor
    Romanovskii, Vladislav
    Zaikovskii, Anatolii
    JOURNAL OF ALGEBRA, 2021, 586 : 99 - 139
  • [10] THE HOMOLOGY OF MATRIX LIE-ALGEBRAS OVER RINGS AND THE HOCHSCHILD HOMOLOGY
    TSYGAN, BL
    RUSSIAN MATHEMATICAL SURVEYS, 1983, 38 (02) : 198 - 199
12345