论文标题
Meromorthic函数的Cochain复合物扩展到繁殖
The extension of cochain complexes of meromorphic functions to multiplications
论文作者
论文摘要
令$ \ mathfrak g $为无限的谎言代数，$ g $是其模块的代数完成。在缝制两个带有许多标记点的Riemann Spher方面，我们使用几何解释，我们在两个空间的元素$ \ Mathcal {M}^K_M（\ Mathfrak G，G，G，G）$和$ \ Mathcal {M}^N_}^N_ {M'}（M Mathfak g，g，g，g，g）$ confimition中引入乘法。参数$（x_1，\ ldots，x_k）$和$（y_1，\ ldots，y_n）$具有特定的分析和对称属性，并且与$ \ Mathfrak g $可值系列相关。这些空间相对于边界 - 探手算子形成了链链络合物。本文的主要结果表明，乘法是由绝对融合的序列定义的，并在空间中取值$ \ mathcal {m}^{k+n} _ {m+m'}（\ mathfrak g，g，g）$。
Let $\mathfrak g$ be an infinite-dimensional Lie algebra and $G$ be the algebraic completion of its module. Using a geometric interpretation in terms of sewing two Riemann spheres with a number of marked points, we introduce a multiplication between elements of two spaces $\mathcal{M}^k_m(\mathfrak g, G)$ and $\mathcal{M}^n_{m'}(\mathfrak g, G)$ of meromorphic functions depending on a number of formal complex parameters $(x_1, \ldots, x_k)$ and $(y_1, \ldots, y_n)$ with specific analytic and symmetry properties, and associated to $\mathfrak g$-valued series. These spaces form a chain-cochain complex with respect to a boundary-coboundary operator. The main result of the paper shows that the multiplication is defined by an absolutely convergent series and takes values in the space $\mathcal{M}^{k+n}_{m+m'}(\mathfrak g, G)$.
