### An explicit construction of the complex of variational calculus and Lie conformal algebra cohomology

Kac, V *(MIT)*

Thursday 26 March 2009, 15:30-16:30

Seminar Room 1, Newton Institute

#### Abstract

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.

#### Video

**The video for this talk should appear here if JavaScript is enabled.**

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.

## Comments

Start the discussion!