Multiplicative vector fields on bundle gerbes
arXiv:2003.12874 · doi:10.1016/j.difgeo.2022.101931
Abstract
Infinitesimal symmetries of -bundle gerbes are modelled with multiplicative vector fields on Lie groupoids. It is shown that a connective structure on a bundle gerbe gives rise to a natural horizontal lift of multiplicative vector fields to the bundle gerbe, and that the 3-curvature presents the obstruction to the horizontal lift being a morphism of Lie 2-algebras. Connection-preserving multiplicative vector fields on a bundle gerbe with connective structure are shown to inherit a natural Lie 2-algebra structure; moreover, this Lie 2-algebra is canonically quasi-isomorphic to the Poisson-Lie 2-algebra of the 2-plectic base manifold , where is the 3-curvature of the connective structure. As an application of this result, we give analogues of a formula of Kostant in the 2-plectic and quasi-Hamiltonian context.
arXiv commentv3: minor edits to improve exposition. 38 pages
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