Abstract
We prove rigorously that the structure constants of the leading (highest spin) linear terms in the commutation relations of the conformal chiral operator algebraW ∞ are identical to those of the Diff 0 + ℝ2 algebra generated by area preserving diffeomorphisms of the plane. Moreover, all quadratic terms of theW N algebra are found to be absent in the limitN→∞. In particular we show thatW ∞ is a central extension of Diff 0 + ℝ2 with non-trivial cocycles appearing only in the commutation relations of its Virasoro subalgebra. We also propose a representation ofW ∞ in terms of a single scalar field in 2+1 dimensions and discuss its significance in the context of quantum field theory.
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