Descent Theory for Vertex Algebras
Robin Mader, Terry Gannon, and Arturo Pianzola
TL;DR
This paper develops a descent theory framework for vertex algebras over differential commutative rings, enabling classification of twisted forms and generalizing known correspondences in the field.
Contribution
It introduces a general descent theory for vertex algebras over differential rings, extending classification and correspondence results.
Findings
Classification of twisted forms of affine vertex algebras
Classification of twisted forms of Heisenberg vertex algebras
Generalization of Li's correspondence
Abstract
Vertex algebras can be defined over any differential commutative ring. We develop the general descent theory for vertex algebras over such bases. We apply this to the classification of twisted forms of affine and Heisenberg vertex algebras, and to reinterpret and generalize a correspondence of Li.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation