论文标题
Poisson顶点的共同体学和泰特谎言谎言代数
Poisson Vertex Cohomology and Tate Lie Algebroids
论文作者
论文摘要
我们研究了环的骨膜上的滑轮，并将其应用于\ cite {bdshk}中定义的复合物的研究，并在Holomorphic Roops to Poisson vertrop的空间上\ emph {poisson vertex algebra}结构的\ emph {poisson vertex algebra}结构进行了处理。我们用$ \ Mathcal {l}^{+} m $的局部紧凑拓扑（Alias \ emph {tate}）滑轮的局部紧凑拓扑（Alias \ emph {tate}）滑轮中相关的谎言式式对象的（连续）de rham-lie共同体描述了这种复合物。特别是，在$π$是符合性的情况下，我们可以轻松地计算上述的共同体 - 我们获得了$ m $的De Rham同谋。
We study sheaves on holomorphic spaces of loops and apply this to the study of the complex, defined in \cite{BdSHK}, governing deformations of the \emph{Poisson vertex algebra} structure on the space of holomorphic loops into a Poisson variety. We describe this complex in terms of the (continuous) de Rham-Lie cohomology of an associated Lie algebroid object in locally linearly compact topological (alias \emph{Tate}) sheaves of modules on $\mathcal{L}^{+}M$. In particular this allows us to easily compute the cohomology of the above in the case where $π$ is symplectic - we obtain de Rham cohomology of $M$.
