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Theoretical analysis reveals convergent pairwise product operations in rational function spaces of grading-restricted vertex algebras, highlighting new structures in their cochain complexes.
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] Γ[Formula: see text] [Formula: see text][Formula: see text] of the corresponding cochain complex. We study properties of two products described above.
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Alexander Zuevsky (2026) studied this question.
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