Multiplicative forms on Poisson groupoids
Zhuo Chen, Honglei Lang, Zhangju Liu

TL;DR
This paper decomposes multiplicative forms on Lie groupoids into characteristic pairs and shows that on Poisson Lie groupoids, these forms form a differential graded Lie algebra, enriching the algebraic structure of such geometric objects.
Contribution
It introduces a decomposition formula for multiplicative forms and establishes a DGLA structure on these forms for Poisson Lie groupoids, linking them to known algebraic frameworks.
Findings
Decomposition of multiplicative forms into characteristic pairs.
Existence of a DGLA structure on multiplicative forms on Poisson Lie groupoids.
Formation of a DGLA crossed module with forms on the base manifold.
Abstract
Given a Lie groupoid over , the tangent Lie algebroid of , and the anchor map, we provide a formula that decomposes an arbitrary multiplicative -form on into two parts. The first part is , a -cocycle of valued in , and the second part is which is -compatible, meaning that for all . We call this pair of data the -characteristic pair of . Next, we prove that if is a Poisson Lie groupoid, then the space of multiplicative forms on has a differential graded Lie algebra (DGLA) structure. Furthermore, when combined with , which is the space of forms on…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
