Gluing data for factorization monoids and vertex ind-schemes

2022/09/20 by Juan Guzmán, Guzmán, Juan
Mathematics · #17B69 #81R10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2209.09952

openalex publication_date 2022/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit description of factorization algebras over the affine line, constructing them from the gluing data determined by its corresponding OPE algebra. We then generalize this construction to factorization monoids, obtaining a description of them in terms of a non-linear version of OPE algebras which we call OPE monoids. In the translation equivariant setting this approach allows us to define vertex ind-schemes, which we interpret as a conformal analogue of the notion of Lie group, since we show that their linearizations yield vertex algebras and that their Zariski tangent spaces are Lie conformal algebras.

Related

• Factorization envelopes and enveloping vertex algebras
• Vertex Algebras and Costello-Gwilliam Factorization Algebras
• On factorization and vector bundles of conformal blocks from vertex algebras
• Some general results on conformal embeddings of affine vertex operator algebras
• Applications of the factorization theorem of conformal blocks to vertex operator algebras