Cohomology of 3-dimensional color Lie algebras

被引:17
作者
Piontkovski, Dmitri
Silvestrov, Sergei D.
机构
[1] Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden
[2] State Univ, Higher Sch Econ, Dept High Math Econ, Moscow 101990, Russia
关键词
color Lie algebras; Koszul algebras; quadratic algebras; cohomology;
D O I
10.1016/j.jalgebra.2006.11.008
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We develop the cohomology theory of color Lie algebras due to Scheunert-Zhang in a framework of non-homogeneous quadratic Koszul algebras. In this approach, the Chevalley-Eilenberg complex of a color Lie algebra becomes a standard Koszul complex for its universal enveloping algebra, providing a constructive method for computation of cohomology. As an application, we compute cohomologies with trivial coefficients of Z(2)(n)-graded 3-dimensional color Lie algebras. 2 (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码:499 / 513
页数:15
相关论文
共 51 条
  • [1] AGRAWALA VK, 1981, HADRONIC J, V4, P444
  • [2] [Anonymous], 2000, BEITR ALG GEOM
  • [3] Backelin Jorgen, 1985, REV ROUMAINE MATH PU, V30, P85
  • [4] Bahturin Yu., 1992, INFINITE DIMENSIONAL
  • [5] Koszul duality patterns in representation theory
    Beilinson, A
    Ginzburg, V
    Soergel, W
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (02) : 473 - 527
  • [6] Poincare-Birkhoff-Witt theorem for quadratic algebras of Koszul type
    Braverman, A
    Gaitsgory, D
    [J]. JOURNAL OF ALGEBRA, 1996, 181 (02) : 315 - 328
  • [7] Representations and cocycle twists of color Lie algebras
    Chen, X. -W.
    Silvestrov, S. D.
    Van Oystaeyen, F.
    [J]. ALGEBRAS AND REPRESENTATION THEORY, 2006, 9 (06) : 633 - 650
  • [8] Note on the cohomology of color Hopf and Lie algebras
    Chen, XW
    Petit, T
    Van Oystaeyen, F
    [J]. JOURNAL OF ALGEBRA, 2006, 299 (01) : 419 - 442
  • [9] Conca A, 2001, MATH SCAND, V89, P201
  • [10] Grobner flags and Gorenstein algebras
    Conca, A
    Rossi, ME
    Valla, G
    [J]. COMPOSITIO MATHEMATICA, 2001, 129 (01) : 95 - 121