Computation of cohomology of Lie conformal and Poisson vertex algebras

Abstract

We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. We establish finite dimensionality of this cohomology for conformal Poisson vertex (super)algebras that are finitely and freely generated by elements of positive conformal weight.

arXiv comment42 pages, revised version with some notational changes

References in corpus (9)

• Cohomology of Conformal Algebras
• Theory of Finite Pseudoalgebras
• Poisson vertex algebras in the theory of Hamiltonian equations
• Freely generated vertex algebras and non-linear Lie conformal algebras
• Lie conformal algebra cohomology and the variational complex
• The variational Poisson cohomology
• Essential variational Poisson cohomology
• An operadic approach to vertex algebra and Poisson vertex algebra cohomology
• Chiral vs classical operad

Cited by in corpus (1)

• Conformal $r$-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and $\mathcal{O}N$-structures