Lie conformal algebra

Summary

A Lie conformal algebra is a module over the polynomial ring $\C[\partial]$ with a $\lambda$-bracket. The values of this bracket are polynomials in a formal variable $\lambda$. It encodes the singular part of the operator product expansion of fields in a vertex operator algebra. Many infinite-dimensional Lie algebras, such as the Virasoro algebra and affine Lie algebras, arise from Lie conformal algebras that are finitely generated over $\C[\partial]$. The notion was introduced by Victor Kac.