Lie conformal algebra cohomology and the variational complex

TL;DR

This paper connects Lie conformal algebra cohomology with the variational complex, providing explicit constructions and a unified understanding of both theories.

Contribution

It introduces explicit constructions of the Lie conformal algebra cohomology complex and the variational complex, revealing their structural relationship.

Findings

Established an interpretation of the variational complex via Lie conformal algebra cohomology

Constructed the Lie conformal algebra cohomology complex explicitly

Provided a structure of a g-complex on the cohomology

Abstract

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a g-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.