论文标题
捆绑胶gerbes上的乘法矢量字段
Multiplicative vector fields on bundle gerbes
论文作者
论文摘要
$ s^1 $ -Bundle Gerbes的无穷小对称性用lie groupoids上的乘法矢量字段进行建模。结果表明，捆绑包上的结缔结构会引起乘数矢量场的自然水平升降，向束gerbe束，并且3个曲度给出了对水平升力的阻塞，是谎言2-翼骨的形态。证明具有连接结构的捆绑包上连接的乘数矢量场，以继承自然的谎言2-代数结构；此外，这个谎言2代数在规范上是2盘基歧管$（m，χ）$的泊松lie 2-代数的准同态，其中$χ$是连接结构的3个外观。作为此结果的应用，我们在2盘和准汉密尔顿语境中给出了Kostant公式的类似物。
Infinitesimal symmetries of $S^1$-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 $(M,χ)$, where $χ$ 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.
