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arXiv · 1904.05319

Affine structures on Lie groupoids

Honglei Lang·Zhangju Liu·Yunhe Sheng
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Abstract

Affine structures on a Lie groupoid, including affine $k$-vector fields, $k$-forms and $(p,q)$-tensors are studied. We show that the space of affine structures is a 2-vector space over the space of multiplicative structures. Moreover, the space of affine multivector fields has a natural graded strict Lie 2-algebra structure and affine (1,1)-tensors constitute a strict monoidal category. Such higher structures can be seen as the categorification of multiplicative structures on a Lie groupoid.

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Honglei Lang, Zhangju Liu, Yunhe Sheng. 2019-04-02. Affine structures on Lie groupoids. https://arxiv.org/abs/1904.05319

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