Calculus structure on the Lie conformal algebra complex and the variational complex

TL;DR

This paper develops a calculus framework on the Lie conformal algebra cochain complex, connecting it to variational calculus and providing explicit formulas for special cases.

Contribution

It introduces a calculus structure on the Lie conformal algebra complex and links it to the variational calculus with explicit formulas.

Findings

Constructed a calculus structure on the Lie conformal algebra cochain complex.

Revealed the connection to the g-complex for degree one chains.

Provided explicit formulas for the variational calculus case.

Abstract

We construct a calculus structure on the Lie conformal algebra cochain complex. By restricting to degree one chains, we recover the structure of a g-complex introduced in [DSK]. A special case of this construction is the variational calculus, for which we provide explicit formulas.