The weak graded Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid (Q6564159)

This paper gives the construction of the weak graded Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid. First, the authors recall the basic notions related to quasi-Poisson groupoids, to weak graded Lie 2-algebra, to differential graded Lie algebra and cubic \(L_\infty\)-algebra. Then the special case of quasi-Poisson groupoids is studied. The authors establish a morphism between the weak graded Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid and the strict Lie 2-algebra of multiplicative multivector fields. They finally determine the associated weak graded Lie 2-algebra structure of IM-forms for any quasi-Lie bialgebroid, which gives a link between Lie 2-algebra theory and quasi Poisson-geometry.