Poisson vertex cohomology and Tate Lie algebroids
Abstract
We study sheaves on holomorphic spaces of loops (also referred to as arcs ) and apply this to the study of the complex, defined in [2], governing deformations of the Poisson vertex algebra structure on the space of holomorphic loops into a Poisson variety. We describe this complex in terms of the (continuous) de Rham–Lie cohomology of an associated Lie algebroid object in locally linearly compact topological (alias Tate ) sheaves of modules on ℒ + M . In particular this allows us to easily compute the cohomology of the above in the case where π is symplectic, we obtain de Rham cohomology of M .
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Annals of representation theory
- Volume
- 3
- Issue
- 1
- Pages
- 99–111
- Publication date
- 16 March 2026
- Language
- EN