Cohomologies of restricted Lie algebras of Hamiltonian vector fields: Computer analysis

Abstract

Restricted algebras, or Lie p-algebras, of vector fields are finite-dimensional analogs of the corresponding classical algebras defined over fields of positive characteristic p. Our computations of p-algebras of Lie vector fields that preserve the symplectic structure (i.e., Hamiltonian and Poisson algebras) revealed important and interesting specific features of the structure of their cohomologies. Explanations of these specific features are presented.