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We construct central extensions of the Lie algebra of differential operators on a one-dimensional affine variety over a field of characteristic zero, generalizing the Virasoro extension. The construction is an application of recent calculations of the Hochschild and cyclic homology of algebras of differential operators.doi:10.1090/s0002-9939-1988-0936774-5 fatcat:g3endz5lmzatxaii2vrrfubhdq