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This article is cited in 3 scientific papers (total in 4 papers)
Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable
A. M. Vershika, B. B. Shoikhetb a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Independent University of Moscow
Abstract:
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.
Citation:
A. M. Vershik, B. B. Shoikhet, “Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable”, TMF, 123:2 (2000), 345–352; Theoret. and Math. Phys., 123:2 (2000), 701–707
Linking options:
https://www.mathnet.ru/eng/tmf608https://doi.org/10.4213/tmf608 https://www.mathnet.ru/eng/tmf/v123/i2/p345
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Abstract page: | 523 | Full-text PDF : | 255 | References: | 60 | First page: | 6 |
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