Glanon groupoids

被引：8
作者：
Lean, Madeleine Jotz [1 ]
Stienon, Mathieu [2 ]
Xu, Ping [2 ]
机构：
[1] Univ Sheffield, Sch Math & Stat, Sheffield, S Yorkshire, England
[2] Penn State Univ, Dept Math, State Coll, PA USA
来源：
MATHEMATISCHE ANNALEN | 2016年 / 364卷 / 1-2期
基金：
瑞士国家科学基金会;
关键词：
GENERALIZED COMPLEX STRUCTURES; POISSON GROUPOIDS; LIE BIALGEBROIDS; CLASSICAL PSEUDOGROUPS; GERSTENHABER ALGEBRAS; SYMPLECTIC GROUPOIDS; MODULAR CLASS; MANIFOLDS; COHOMOLOGY; GEOMETRY;
D O I：
10.1007/s00208-015-1222-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce the notions of Glanon groupoids, which are Lie groupoids equipped with multiplicative generalized complex structures, and of Glanon algebroids, their infinitesimal counterparts. Both symplectic and holomorphic Lie groupoids are particular instances of Glanon groupoids. We prove that there is a bijection between Glanon algebroids on one hand and source connected and source-simply connected Glanon groupoids on the other. As a consequence, we recover various known integrability results and obtain the integration of holomorphic Lie bialgebroids to holomorphic Poisson groupoids.
引用
收藏
页码：485 / 518
页数：34
相关论文
共 41 条
[1]  
Alekseev A., 2001, COURANT ALGEBR UNPUB
[2]  
[Anonymous], 1987, P INT C MATH
[3]  
[Anonymous], 2003, THESIS
[4]  
[Anonymous], 1973, Pure and Applied Mathematics
[5]  
Barton J, 2008, PAC J MATH, V236, P22
[6]   Tangent of a Courant algebroid [J].
Boumaiza, Mohamed ;
Zaalani, Nadhem .
COMPTES RENDUS MATHEMATIQUE, 2009, 347 (3-4) :177-182
[7]   KV-cohomology of Koszul-Vinberg algebroids and Poisson manifolds [J].
Boyom, MN .
INTERNATIONAL JOURNAL OF MATHEMATICS, 2005, 16 (09) :1033-1061
[8]  
Bursztyn H., ARXIV14105135
[9]  
Cattaneo AS, 2001, PROG MATH, V198, P61
[10]  
Coste A., 1987, Publ. Dep. Math. Nouvelle Ser. A, V2, P1
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