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.
@article{TMF_2000_123_2_a14,
author = {A. M. Vershik and B. B. Shoikhet},
title = {Graded {Lie} algebras whose {Cartan} subalgebra is the algebra of polynomials in one variable},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {345--352},
publisher = {mathdoc},
volume = {123},
number = {2},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a14/}
}
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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/