2019/11/05 by Cliff, Emily
#17B69 #81R10 #81T40 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1911.01627
We recall Borcherds's approach to vertex algebras via "singular commutative rings", and introduce new examples of his constructions which we compare to vertex algebras, chiral algebras, and factorization algebras. We show that all vertex algebras (resp. chiral algebras or equivalently factorization algebras) can be realized in these new categories VA(A,H,S), but we also show that the functors from VA(A,H,S) to vertex algebras or chiral algebras are not equivalences: a single vertex or chiral algebra may have non-equivalent realizations as an (A, H,S)-vertex algebra.