TY - JOUR
T1 - Glanon groupoids
AU - Lean, Madeleine Jotz
AU - Stiénon, Mathieu
AU - Xu, Ping
N1 - Funding Information:
Research partially supported by a Dorothea-Schlözer fellowship of the University of Göttingen, Swiss NSF Grants 200021-121512 and PBELP2_137534, NSF Grants DMS-0801129 and DMS-1101827, NSA Grant H98230-12-1-0234.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00208-015-1222-z
DO - 10.1007/s00208-015-1222-z
M3 - Article
AN - SCOPUS:84955712250
SN - 0025-5831
VL - 364
SP - 485
EP - 518
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -