The weak graded Lie 2-algebra ofmultiplicative forms on a quasi-poissongroupoid | BIMSA General Lecture

Abstract

We present a construction ofweak graded Lie 2-algebras associated with quasi-Poissongroupoids. We also establish a morphism between this weak graded Lie 2-algebra of multiplicativeforms and the strict graded Lie 2-algebra of multiplicative multivector fields, allowing us to compareand relate different aspects of Lie 2-algebra theory within the context of quasi-Poisson geometry. Asan infinitesimal analogy, we explicitly determine the associated weak graded Lie 2-algebra structureof IM forms along with differential forms on the base manifold for any quasi-Lie bialgebroid.