AREA-PRESERVING DIFFEOMORPHISMS AND HIGHER-SPIN ALGEBRAS

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonic d=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphere S2 as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic space S1,1, and can be rewritten as {Mathematical expression}. As an application of our results, we formulate a new d=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms of S1,1. © 1990 Springer-Verlag.