The extension of cochain complexes of meromorphic functions to multiplications

2022/08/22 by Levin, Daniel, Zuevsky, Alexander
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2208.10071

Abstract

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 M^k_m(\mathfrak g, G) and Mⁿ_m'(\mathfrak g, G) of meromorphic functions depending on a number of formal complex parameters (x₁, …, x_k) and (y₁, …, 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 M^k+n_m+m'(\mathfrak g, G).

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