Lie-nijenhuis Bialgebroids

被引：2
|
作者：
Drummond, Thiago [1 ]
机构：
[1] Univ Fed Rio de Janeiro, Inst Matemat, Dept Matemat, Caixa Postal 68530, BR-21941909 Rio De Janeiro, RJ, Brazil
来源：
QUARTERLY JOURNAL OF MATHEMATICS | 2022年 / 73卷 / 03期
关键词：
POISSON; GROUPOIDS; TANGENT; LIFTS;
D O I：
10.1093/qmath/haab048
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce Lie-Nijenhuis bialgebroids as Lie bialgebroids endowed with an additional derivation-like object. They give a complete infinitesimal description of Poisson-Nijenhuis (PN) groupoids, and key examples include PN manifolds, holomorphic Lie bialgebroids and flat Lie bialgebra bundles. To achieve our goal we develop a theory of 'generalized derivations' and their duality, extending the well-established theory of derivations on vector bundles.
引用
收藏
页码：849 / 883
页数：35
相关论文
共 50 条
  • [31] Modular Classes of Poisson–Nijenhuis Lie Algebroids
    Raquel Caseiro
    Letters in Mathematical Physics, 2007, 80 : 223 - 238
  • [32] Lie groupoids and the Frolicher-Nijenhuis bracket
    Bursztyn, Henrique
    Drummond, Thiago
    BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2013, 44 (04): : 709 - 730
  • [33] Nijenhuis Operators on n-Lie Algebras
    Liu, Jie-Feng
    Sheng, Yun-He
    Zhou, Yan-Qiu
    Bai, Cheng-Ming
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2016, 65 (06) : 659 - 670
  • [34] Modular classes of Poisson-Nijenhuis Lie algebroids
    Caseiro, Raquel
    LETTERS IN MATHEMATICAL PHYSICS, 2007, 80 (03) : 223 - 238
  • [35] Horn-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids
    Cai, Liqiang
    Liu, Jiefeng
    Sheng, Yunhe
    JOURNAL OF GEOMETRY AND PHYSICS, 2017, 121 : 15 - 32
  • [36] Lie groupoids and the Frölicher-Nijenhuis bracket
    Henrique Bursztyn
    Thiago Drummond
    Bulletin of the Brazilian Mathematical Society, New Series, 2013, 44 : 709 - 730
  • [37] Invariant Poisson-Nijenhuis structures on Lie groups and classification
    Ravanpak, Zohreh
    Rezaei-Aghdam, Adel
    Haghighatdoost, Ghorbanali
    INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2018, 15 (04)
  • [38] Nijenhuis-operator on Hom-Lie conformal algebras
    Asif, Sania
    Wang, Yao
    Yuan, Lamei
    TOPOLOGY AND ITS APPLICATIONS, 2024, 344
  • [39] A Note on Multi-Oriented Graph Complexes and Deformation Quantization of Lie Bialgebroids
    Morand, Kevin
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2022, 18
  • [40] THE CONSTRUCTIONS AND DEFORMATIONS OF NIJENHUIS OPERATORS ON 3-HOM-LIE ALGEBRAS
    Li, Yizheng
    Wang, Dingguo
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2025, 62 (01) : 127 - 143
12345