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Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 345-352
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We define a class of infinite-dimensional Lie algebras that generalize the universal enveloping algebra of the algebra $sl(2,\mathbb C)$ regarded as a Lie algebra. These algebras are a special case of $\mathbb Z$-graded Lie algebras with a continuous root system, namely, their Cartan subalgebra is the algebra of polynomials in one variable. The continuous limit of these algebras defines new Poisson brackets on algebraic surfaces. 
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A. M. Vershik; B. B. Shoikhet. Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 345-352. http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a14/

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