Abstract:
We construct Lie algebras of vector fields on universal bundles of symmetric squares of hyperelliptic curves of genus g=1,2,…g=1,2,….
For each of these Lie algebras, the Lie subalgebra of vertical fields has commuting generators, while the generators of the Lie subalgebra of projectable fields determines the canonical representation of the Lie subalgebra with generators L2q, q=−1,0,1,2,…, of the Witt algebra.
As an application, we obtain integrable polynomial dynamical systems.
Keywords:
infinite-dimensional Lie algebras, representations of the Witt algebra, symmetric polynomials, symmetric powers of curves, commuting operators, polynomial dynamical systems.
Citation:
V. M. Buchstaber, A. V. Mikhailov, “Infinite-Dimensional Lie Algebras Determined by the Space of Symmetric Squares of Hyperelliptic Curves”, Funktsional. Anal. i Prilozhen., 51:1 (2017), 4–27; Funct. Anal. Appl., 51:1 (2017), 2–21
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\paper Infinite-Dimensional Lie Algebras Determined by the Space of Symmetric Squares of Hyperelliptic Curves
\jour Funktsional. Anal. i Prilozhen.
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\pages 4--27
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\vol 51
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Linking options:
https://www.mathnet.ru/eng/faa3260
https://doi.org/10.4213/faa3260
https://www.mathnet.ru/eng/faa/v51/i1/p4
This publication is cited in the following 10 articles:
V. M. Buchstaber, E. Yu. Bunkova, “Hyperelliptic Sigma Functions and Adler–Moser Polynomials”, Funct. Anal. Appl., 55:3 (2021), 179–197
V. M. Buchstaber, E. Yu. Bunkova, “Lie Algebras of Heat Operators in a Nonholonomic Frame”, Math. Notes, 108:1 (2020), 15–28
Takanori Ayano, Victor M. Buchstaber, “Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3”, SIGMA, 15 (2019), 032, 15 pp.
E. Yu. Bunkova, “On the problem of differentiation of hyperelliptic functions”, Eur. J. Math., 5:3, SI (2019), 712–719
E. Yu. Bunkova, “Differentiation of genus 3 hyperelliptic functions”, Eur. J. Math., 4:1 (2018), 93–112
O. K. Sheinman, “Integrable Systems of Algebraic Origin and Separation of Variables”, Funct. Anal. Appl., 52:4 (2018), 316–320
V. M. Buchstaber, A. V. Mikhailov, “Polynomial Hamiltonian integrable systems on symmetric powers of plane curves”, Russian Math. Surveys, 73:6 (2018), 1122–1124
V. M. Buchstaber, V. I. Dragovich, “Two-Valued Groups, Kummer Varieties, and Integrable Billiards”, Arnold Math. J., 4:1 (2018), 27–57
O. K. Sheinman, “Almost graded current algebras on the symmetric square of a curve”, Russian Math. Surveys, 72:2 (2017), 384–386
T. Ayano, V. M. Buchstaber, “The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications”, Funct. Anal. Appl., 51:3 (2017), 162–176
Citation in format AMSBIB
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