Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable |
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Authors: | A M Vershik B B Shoikhet |
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Institution: | (1) St. Petersburg Division, Steklov Mathematical Institute, RAS, St. Petersburg, Russia;(2) Independent University of Moscow, Moscow, Russia |
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Abstract: | 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 algebra. These algebras are a special case of 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.
In memory of M. V. Saveliev
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 345–352, May, 2000. |
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