Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable

We define a class of infinite-dimensional Lie algebras that generalize the universal enveloping algebra of the algebra sl(2, C) regarded as a Lie alge bra. These algebras are a special case of Z-graded Lie algebras with a. con tinuous root system, namely, their Cartan subalgebra is the algebra of poly nomials in one variable. The continuous limit of these algebras defines new Poisson brackets on algebraic surfaces.