Multiplicative forms on Poisson groupoids

作     者：Zhuo Chen Honglei Lang Zhangju Liu 

作者机构：Department of Mathematical Sciences Tsinghua University College of Science China Agricultural University School of Mathematics and Statistics Henan University 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.12071241) the National Key Research and Development Program of China (Grant No.2021YFA1002000) 

摘      要：First, we prove a decomposition formula for any multiplicative differential form on a Lie groupoid G. Next, we prove that if G is a Poisson Lie groupoid, then the space Ω·mult(G) of multiplicative forms on G has a differential graded Lie algebra(DGLA) structure. Furthermore, when combined with Ω·(M), which is the space of forms on the base manifold M of G, Ω·mult(G) forms a canonical DGLA crossed module. This supplements a previously known fact that multiplicative multi-vector fields on G form a DGLA crossed module with the Schouten algebra Γ(∧·A) stemming from the Lie algebroid A of G.