SYMMETRIES AND LIE-ALGEBRAS OF THE HARRY-DYM HIERARCHY

For the Harry Dym equation, there exist four sets of time-independent symmetries and one set of the master symmetries. The negative half-hie rarchy of the master symmetries are also the time-independent symmetri es. All these symmetries constitute an infinite-dimensional Lie algebr a. Four hierarchies of integrable models possess one common recursion operator and one set of common symmetries. Only usual Harry Dym hierar chy, which contains the Harry Dym equation, possesses four sets of tim e-independent symmetries, while other three integrable hierarchies pos sess only two sets of time-independent symmetries.