Chiral homology of the projective line and extensions of vertex algebra modules

2024/08/12 by Cardoso, Thadeu Henrique, van Ekeren, Jethro, Guzman, Juan +1
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2408.06444

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 one dimensional projective space with coefficients in the corresponding chiral algebra.

Related

• The First Chiral Homology Group
• The first chiral homology group in higher genus
• Conformal field theories associated to regular chiral vertex operator algebras I: theories over the projective line
• A Hodge filtration on chiral homology and Poisson homology of associated schemes
• Higher Chiral Algebras in a Polysimplicial Model