An explicit construction of the complex of variational calculus and Lie conformal algebra cohomology
Seminar Room 1, Newton Institute
Lie conformal algebras encode the singular part of the operator product expansion of chiral fields in conformal field theory, and, at the same time, the local Poisson brackets in the theory of soliton equations. That is why they form an essential part of the vertex algebra and Poisson vertex algebra theories. The structure and cohomology theory of Lie conformal algebras was developed about 10 years ago. In a recent joint work with Alberto De Sole we show that the Lie conformal algebra cohomology can be used to explicitly construct the complex of calculus of variations, which is the resolution of the variational derivative map of Euler and Lagrange.