论文标题
顶点代数的共同体学计算
Computation of cohomology of vertex algebras
论文作者
论文摘要
我们回顾了与手性和古典作业相对应的共同体理论。第一个是顶点代数的共同体理论，而第二个是泊松顶点代数（PVA）的经典协同学，我们构建了与它们相关的光谱序列。由于在“良好”情况下，经典的PVA共同体与各种PVA的同一个共同体相吻合，并且有发达的方法可以计算后者，因此在许多有趣的情况下，这使我们能够计算顶点代数的共同体。最后，我们通过消失的第一个共同体来描述一种统一的集成性方法，该方法适用于哈密顿PDE的经典和量子系统。
We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct a spectral sequence relating them. Since in "good" cases the classical PVA cohomology coincides with the variational PVA cohomology and there are well-developed methods to compute the latter, this enables us to compute the cohomology of vertex algebras in many interesting cases. Finally, we describe a unified approach to integrability through vanishing of the first cohomology, which is applicable to both classical and quantum systems of Hamiltonian PDEs.
