An introduction to pseudoalgebras

The concept of Lie pseudoalgebra over a cocommutative Hopf algebra is a generalization of that of a Lie algebra. The basic motivating example is provided by the algebra underlying Operator Product Expansion of fields in a vertex algebra, i.e., in the chiral part of a Conformal Field Theory. I give a short introduction to the algebraic structures of vertex algebras and pseudoalgebras, introduce the basic tools used in the theory, and list the main results of the theory of finite Lie pseudoalgebras. A few applications are given.