Deformations of Vector Bundles over Lie Groupoids

Pier Paolo La Pastina; Luca Vitagliano

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arXiv · 1907.05670

Deformations of Vector Bundles over Lie Groupoids

Pier Paolo La Pastina·Luca Vitagliano

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Abstract

VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including Lie group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term representations up to homotopy of Lie groupoids. We attach to every VB-groupoid a cochain complex controlling its deformations and discuss its fundamental features, such as Morita invariance and a van Est theorem. Several examples and applications are given.

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Pier Paolo La Pastina, Luca Vitagliano. 2019-07-12. Deformations of Vector Bundles over Lie Groupoids. https://arxiv.org/abs/1907.05670

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