Hamiltonian Algebroid Symmetries in W-Gravity and Poisson Sigma-Model

摘要

Starting from a Lie algebroid Alpha over a space Psi the authors lift its actionto the canonical transformations on the principle affine bundle R over the contangent bundle Tau(star)Psi. Such lifts are classified by the first cohomology Eta(sup 1)(Alpha). The resulting object is the Hamiltonian algebroid Alpha(sup Eta) over R with the anchor map from Gamma(Alpha(sup Eta)) to Hamiltonians of canonical transformations. Hamiltonian algebroids generalize the Lie algebras of canonical transformations.