The product on 𝒱-spaces of rational functions

Abstract

Let [Formula: see text] be a grading-restricted vertex algebra, and [Formula: see text] be the algebraic completion of the space of [Formula: see text]-valued rational functions with complex parameters [Formula: see text], [Formula: see text]. We consider two subspaces [Formula: see text] and [Formula: see text] of [Formula: see text], [Formula: see text], [Formula: see text], such that a pairwise product introduced for their elements converges with respect to a complex parameter, and represents a linear map [Formula: see text]. A product is introduced also for elements of two spaces [Formula: see text] ×[Formula: see text] [Formula: see text][Formula: see text] of the corresponding cochain complex. We study properties of two products described above.