CURRENT-ALGEBRAS OVER MANIFOLDS - POISSON ALGEBRAS, Q-DEFORMATIONS AND QUANTIZATION

Poisson algebras on current manifolds (of maps from a finite-dimension al manifold into a two-dimensional manifold) are investigated using sy mplectic geometry. It is shown that there is a one to-one corresponden ce between such current manifolds and Poisson current algebras with th ree generators. A geometric meaning is given to q-deformations of curr ent algebras. The geometric quantization of current algebras and quant um current algebraic maps is also studied. (C) 1998 Elsevier Science B .V.