Work

Chiral Homology of the Projective Line and Extensions of Vertex Algebra Modules

Year: 2026

Type: article

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.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-026-05749-4

Authors: Thadeu Henrique Cardoso, Jethro van Ekeren, Juan Guzman, Reimundo Heluani

Institution: Instituto Nacional de Matemática Pura e Aplicada

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990