w_infty Algebras and w_infty Gravity Area-Preserving Diffeomorphisms

The w_infty algebra is a particular generalization of the Virasoro algebra with generators of higher spin 2,3,...,infty. It can be viewed as the algebra of a class of functions, relative to a Poisson bracket, on a suitably chosen surface. Thus, w_infty is a special case of area-preserving diffeomorphisms of an arbitrary surface. We review various aspects of area- preserving diffeomorphisms, w_infty algebras and w_infty gravity. The topics covered include a) the structure of the algebra of area-preserving diffeomorphisms with central extensions and their relation to w_infty algebras, b) various generalizations of w_infty algebras, c) the structure of w_infty gravity and its geometrical aspects, d) nonlinear realizations of w_infty symmetry and e) various quantum realizations of w_infty symmetry.

Area-Preserving Diffeomorphisms, w_infty Algebras and w_infty Gravity Institutional Repository Document