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 spaceΩ_(mult)·(G)of multiplicative forms on G has a ...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 spaceΩ_(mult)·(G)of multiplicative forms on G has a differential graded Lie algebra(DGLA)structure.Furthermore,when combined withΩ·(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 algebraΓ(∧·A)stemming from the Lie algebroid A of G.展开更多
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).
文摘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 spaceΩ_(mult)·(G)of multiplicative forms on G has a differential graded Lie algebra(DGLA)structure.Furthermore,when combined withΩ·(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 algebraΓ(∧·A)stemming from the Lie algebroid A of G.
