A NEW HIGHER-SPIN ALGEBRA AND THE LONE-STAR PRODUCT

In two recent papers, we constructed a new N→∞ limit of the WN algebras, which we denote W∞ having generators of conformal spins 2, 3, ..., with central terms for all spins. In this paper, we constrct another new algebra, which we denote W1+∞, with generators of conformal spins, 1, 2, 3, ..., again with central terms for all spins. The requirement that the algebras be closed requires that one include the spin-1 generators in W1+∞, and prohibits their inclusion in W∞. Paralleling our analogous construction for W∞, we show that the new algebra can also be realised as the antisymmetric part of an associative "lone-star" product, which also closes on the set of generators with conformal spins ≥1. © 1990.