The weak Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid

Zhuo Chen; Honglei Lang; Zhangju Liu

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arXiv · 2302.01294

The weak Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid

Zhuo Chen·Honglei Lang·Zhangju Liu

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Abstract

Berwick-Evens and Lerman recently showed that the category of vector fields on a geometric stack has the structure of a Lie $2$-algebra. Motivated by this work, we present a construction of graded weak Lie $2$-algebras associated with quasi-Poisson groupoids based on the space of multiplicative forms on the groupoid and differential forms on the base manifold. We also establish a morphism between the Lie $2$-algebra of multiplicative multivector fields and the weak Lie $2$-algebra of multiplicative forms, allowing us to compare and relate different aspects of Lie $2$-algebra theory within the context of quasi-Poisson geometry. As an infinitesimal analogy, we explicitly determine the associated weak Lie $2$-algebra structure of IM $1$-forms along with differential $1$-forms on the base manifold for any quasi-Lie bialgebroid.

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BibTeX RIS

Zhuo Chen, Honglei Lang, Zhangju Liu. 2023-01-27. The weak Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid. https://arxiv.org/abs/2302.01294

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