Lie theory of vector bundles, Poisson geometry and double structures
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
TL;DR
This paper reviews the Lie theoretical framework of vector bundles over Lie groupoids and algebroids, emphasizing the role of Poisson geometry in extending these concepts to double structures like LA-groupoids.
Contribution
It highlights the role of Poisson geometry in extending Lie theory to double Lie algebroids and LA-groupoids, providing a unifying perspective.
Findings
Clarifies the Lie theory underlying vector bundles over Lie groupoids and algebroids.
Shows how Poisson geometry extends these results to double structures.
Provides insights into the structure of LA-groupoids and double Lie algebroids.
Abstract
We briefly review our results on the Lie theory underlying vector bundles over Lie groupoids and Lie algebroids, pointing out the role of Poisson geometry in extending these results to double Lie algebroids and LA-groupoids.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Algebra and Geometry