Vector bundles over Lie groupoids and algebroids

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• 作者：Henrique Bursztyn^a ; ^{henrique@impa.br" class="auth_mail" title="E-mail the corresponding author} ; Alejandro Cabrera^b ; ^{acabrera@labma.ufrj.br" class="auth_mail" title="E-mail the corresponding author} ; Matias del Hoyo^a ; ^{mdelhoyo@impa.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：VB-groupoids ; VB-algebroids ; LA-groupoids ; Double Lie algebroids ; Poisson groupoids
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：26 February 2016
• 年：2016
• 卷：290
• 期：Complete
• 页码：163-207
• 全文大小：730 K

文摘

We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their relation via differentiation and integration. We also show how to extend our techniques to describe the more general Lie theory underlying double Lie algebroids and LA-groupoids.