Differential Graded Lie Algebras and Leibniz Algebra Cohomology

被引：2
|
作者：
Mostovoy, Jacob [1 ]
机构：
[1] Cinvestav, Dept Matemat, Ciudad De Mexico, Mexico
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 01期
关键词：
D O I：
10.1093/imrn/rnaa086
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, we interpret Leibniz algebras as differential graded (DG) Lie algebras. Namely, we consider two fully faithful functors from the category of Leibniz algebras to that of DG Lie algebras and show that they naturally give rise to the Leibniz cohomology and the Chevalley-Eilenberg cohomology. As an application, we prove a conjecture stated by Pirashvili in [9].
引用
收藏
页码：196 / 209
页数：14
相关论文
共 50 条
  • [1] Cohomology jump loci of differential graded Lie algebras
    Budur, Nero
    Wang, Botong
    [J]. COMPOSITIO MATHEMATICA, 2015, 151 (08) : 1499 - 1528
  • [2] Differential graded cohomology and Lie algebras of holomorphic vector fields
    Wagemann, F
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 208 (02) : 521 - 540
  • [3] Differential Graded Cohomology and Lie Algebras¶of Holomorphic Vector Fields
    Friedrich Wagemann
    [J]. Communications in Mathematical Physics, 1999, 208 : 521 - 540
  • [4] About Leibniz cohomology and deformations of Lie algebras
    Fialowski, A.
    Magnin, L.
    Mandal, A.
    [J]. JOURNAL OF ALGEBRA, 2013, 383 : 63 - 77
  • [5] GRADED LIE ALGEBRAS OF AN ALGEBRA
    NIJENHUIS, A
    [J]. PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1967, 70 (05): : 475 - +
  • [6] Graded Lie Algebras and Intersection Cohomology
    Lusztig, G.
    [J]. REPRESENTATION THEORY OF ALGEBRAIC GROUPS AND QUANTUM GROUPS, 2010, 284 : 191 - 224
  • [7] COHOMOLOGY AND DEFORMATIONS IN GRADED LIE ALGEBRAS
    NIJENHUI.A
    RICHARDS.RW
    [J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 72 (1P1): : 1 - &
  • [8] New applications of graded Lie algebras to Lie algebras, generalized Lie algebras, and cohomology
    Pinczon, Georges
    Ushirobira, Rosane
    [J]. JOURNAL OF LIE THEORY, 2007, 17 (03) : 633 - 667
  • [9] DIFFERENTIAL GRADED LIE GROUPS AND THEIR DIFFERENTIAL GRADED LIE ALGEBRAS
    Jubin, Benoit
    Kotov, Alexei
    Poncin, Norbert
    Salnikov, Vladimir
    [J]. TRANSFORMATION GROUPS, 2022, 27 (02) : 497 - 523
  • [10] DIFFERENTIAL GRADED LIE GROUPS AND THEIR DIFFERENTIAL GRADED LIE ALGEBRAS
    BENOIT JUBIN
    ALEXEI KOTOV
    NORBERT PONCIN
    VLADIMIR SALNIKOV
    [J]. Transformation Groups, 2022, 27 : 497 - 523
12345