IDEALS OF KAC-MOODY ALGEBRAS AND REALIZATIONS OF W-INFINITY
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We have recently constructed two new higher-spin extensions of the Virasoro algebra, denoted W1+ and W, with generators of all conformal spins s1 and s2 respectively, which admit central terms for all spins. In this paper, we show how these algebras may, respectively, be realised as enveloping algebras of the U(1) Kac-Moody algebra and the Virasoro algebra, factored by certain ideals. The algebra W1+ may be viewed as the algebra of all smooth differential operators on the circle. 1990.