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 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.

56 pages

References in corpus (2)

• Cohomology of Conformal Algebras
• Theory of Finite Pseudoalgebras

Cited by in corpus (9)

• The variational Poisson cohomology
• Non-local Poisson structures and applications to the theory of integrable systems
• Essential variational Poisson cohomology
• An operadic approach to vertex algebra and Poisson vertex algebra cohomology
• On the Ado Theorem for finite Lie conformal algebras with Levi decomposition
• Computation of cohomology of Lie conformal and Poisson vertex algebras
• Calculus structure on the Lie conformal algebra complex and the variational complex
• Double Multiplicative Poisson Vertex Algebras
• Conformal $r$-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and $\mathcal{O}N$-structures