Chiral Homology of the Projective Line and Extensions of Vertex Algebra Modules
Abstract The purpose of this note is to establish an isomorphism from the vector space of extensions between two modules over a vertex algebra, to an appropriate first chiral homology of the projective line with coefficients in the corresponding chiral algebra. This yields, in particular, a homological criterion for rationality of vertex algebras.
Authors
- Reimundo Heluani (ORCID: https://orcid.org/0000-0002-4203-4693)
- Jethro van Ekeren (ORCID: https://orcid.org/0000-0003-0073-3549)
- Thadeu Henrique Cardoso
- Juan Guzmán
Institutions
- Instituto Nacional de Matemática Pura e Aplicada (BR)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2026-10-28
- DOI
- https://doi.org/10.1007/s00220-026-05749-4
- Primary Topic
- Algebraic structures and combinatorial models
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- Instituto Nacional de Ciência e Tecnologia de Matemática