Deformations of Lie Groupoids

被引：9

作者：

Crainic, Marius ^{[1
]}

Mestre, Joao Nuno ^{[1
]}

Struchiner, Ivan ^{[2
]}

机构：

[1] Univ Utrecht, Dept Math, NL-3508 TA Utrecht, Netherlands

[2] Univ Sao Paulo, Dept Math, Sao Paulo, Brazil

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2020年 / 2020卷 / 21期

基金：

欧洲研究理事会; 巴西圣保罗研究基金会;

关键词：

REPRESENTATIONS; COHOMOLOGY; LINEARIZATION; HOMOTOPY; BRACKETS;

D O I：

10.1093/imrn/rny221

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance, a van Est theorem, and a vanishing result in the proper case. Combined with Moser's deformation arguments for groupoids, we obtain several rigidity and normal form results.

引用

页码：7662 / 7746

页数：85

共 50 条

[1] Deformations of vector bundles over Lie groupoids
La Pastina, Pier Paolo
Vitagliano, Luca
[J]. REVISTA MATEMATICA COMPLUTENSE, 2023, 36 (03): : 933 - 971
[2] Deformations of vector bundles over Lie groupoids
Pier Paolo La Pastina
Luca Vitagliano
[J]. Revista Matemática Complutense, 2023, 36 : 933 - 971
[3] Homology of formal deformations of proper etale Lie groupoids
Neumaier, N.
Pflaum, M. J.
Posthuma, H. B.
Tang, X.
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2006, 593 : 117 - 168
[4] From double Lie groupoids to local Lie 2-groupoids
Rajan Amit Mehta
Xiang Tang
[J]. Bulletin of the Brazilian Mathematical Society, New Series, 2011, 42 : 651 - 681
[5] From double Lie groupoids to local Lie 2-groupoids
Mehta, Rajan Amit
Tang, Xiang
[J]. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2011, 42 (04): : 651 - 681
[6] INTEGRABILITY OF LIE GROUPOIDS
ABIB, OR
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1973, 276 (26): : 1693 - 1695
[7] Prolongations of Lie groupoids and Lie algebroids
Saunders, DJ
[J]. HOUSTON JOURNAL OF MATHEMATICS, 2004, 30 (03): : 637 - 655
[8] LIE GROUPOIDS AND THEIR ALGEBROIDS
Cartier, Pierre
[J]. ASTERISQUE, 2009, (326) : 165 - 196
[9] On fibrations of Lie groupoids
Chen, Bohui
Du, Cheng-Yong
Wang, Yu
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2020, 152
[10] Lie algebroids, Lie groupoids and TFT
Bonechi, Francesco
Zabzine, Maxim
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2007, 57 (03) : 731 - 744

← 1 2 3 4 5 →