Non-abelian homology of Lie algebras

被引：12
|
作者：
Inassaridze, N
Khmaladze, E
Ladra, M
机构：
[1] Georgian Acad Sci, A Razmadze Math Inst, GE-0193 Tbilisi, Georgia
[2] Univ Santiago de Compostela, Fac Math, Dept Algebra, Santiago De Compostela 15782, Spain
来源：
GLASGOW MATHEMATICAL JOURNAL | 2004年 / 46卷
关键词：
D O I：
10.1017/S0017089504001909
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Non-abelian homology of Lie algebras with coefficients in Lie algebras is constructed and studied, generalising the classical Chevalley-Eilenberg homology of Lie algebras. The relationship between cyclic homology and Milnor cyclic homology of non-commutative associative algebras is established in terms of the long exact non-abelian homology sequence of Lie algebras. Some explicit formulae for the second and the third non-abelian homology of Lie algebras are obtained.
引用
收藏
页码：417 / 429
页数：13
相关论文
共 50 条
  • [1] NON-ABELIAN HOMOLOGY OF HOM-LIE ALGEBRAS AND APPLICATIONS
    Casas, J. M.
    Khmaladze, E.
    Rego, N. Pacheco
    PROCEEDINGS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2015, 167 : 99 - 106
  • [2] NON-ABELIAN EXTERIOR PRODUCTS OF LIE-ALGEBRAS AND AN EXACT SEQUENCE IN THE HOMOLOGY OF LIE-ALGEBRAS
    ELLIS, GJ
    JOURNAL OF PURE AND APPLIED ALGEBRA, 1987, 46 (2-3) : 111 - 115
  • [3] Non-abelian cohomology and extensions of lie algebras
    Inassaridze, N.
    Khmaladze, E.
    Ladra, M.
    JOURNAL OF LIE THEORY, 2008, 18 (02) : 413 - 432
  • [4] On the non-abelian tensor product of Lie algebras
    Salemkar, Ali Reza
    Tavallaee, Hamid
    Mohammadzadeh, Hamid
    Edalatzadeh, Behrouz
    LINEAR & MULTILINEAR ALGEBRA, 2010, 58 (03): : 333 - 341
  • [5] Non-Abelian extensions of topological lie algebras
    Neeb, KH
    COMMUNICATIONS IN ALGEBRA, 2006, 34 (03) : 991 - 1041
  • [6] Non-abelian tensor product and homology of Lie superalgebras
    Garcia-Martinez, Xabier
    Khraaladze, Emzar
    Ladra, Manuel
    JOURNAL OF ALGEBRA, 2015, 440 : 464 - 488
  • [7] A non-abelian exterior product and homology of Leibniz algebras
    Donadze, Guram
    Garcia-Martinez, Xabier
    Khmaladze, Emzar
    REVISTA MATEMATICA COMPLUTENSE, 2018, 31 (01): : 217 - 236
  • [8] A non-abelian exterior product and homology of Leibniz algebras
    Guram Donadze
    Xabier García-Martínez
    Emzar Khmaladze
    Revista Matemática Complutense, 2018, 31 : 217 - 236
  • [9] A NON-ABELIAN TENSOR PRODUCT OF LIE-ALGEBRAS
    ELLIS, GJ
    GLASGOW MATHEMATICAL JOURNAL, 1991, 33 : 101 - 120
  • [10] A Non-abelian Tensor Product of Hom–Lie Algebras
    J. M. Casas
    E. Khmaladze
    N. Pacheco Rego
    Bulletin of the Malaysian Mathematical Sciences Society, 2017, 40 : 1035 - 1054
12345