Lie Conformal Algebra Cohomology and the Variational Complex

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 par- ticular, 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 con- struction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.