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Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 1, Pages 4–27 (Mi faa3260)  

This article is cited in 7 scientific papers (total in 7 papers)

Infinite-Dimensional Lie Algebras Determined by the Space of Symmetric Squares of Hyperelliptic Curves

V. M. Buchstabera, A. V. Mikhailovb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b University of Leeds, Department of Applied Mathematics

Abstract: We construct Lie algebras of vector fields on universal bundles of symmetric squares of hyperelliptic curves of genus $g=1,2,…$. 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 $L_{2q}$, $q=-1, 0, 1, 2, …$, 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

Funding Agency Grant Number
Royal Society
The work was supported by the Royal Society International Exchanges Scheme Grant.


DOI: https://doi.org/10.4213/faa3260

Full text: PDF file (308 kB)
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English version:
Functional Analysis and Its Applications, 2017, 51:1, 2–21

Bibliographic databases:

UDC: 512.554.32+517
Received: 20.10.2016
Accepted:20.10.2016

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. K. Sheinman, “Almost graded current algebras on the symmetric square of a curve”, Russian Math. Surveys, 72:2 (2017), 384–386  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    3. E. Yu. Bunkova, “Differentiation of genus 3 hyperelliptic functions”, Eur. J. Math., 4:1 (2018), 93–112  crossref  mathscinet  zmath  isi  scopus
    4. O. K. Sheinman, “Integrable Systems of Algebraic Origin and Separation of Variables”, Funct. Anal. Appl., 52:4 (2018), 316–320  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. M. Buchstaber, A. V. Mikhailov, “Polynomial Hamiltonian integrable systems on symmetric powers of plane curves”, Russian Math. Surveys, 73:6 (2018), 1122–1124  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. 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.  mathnet  crossref  mathscinet
    7. V. M. Buchstaber, E. Yu. Bunkova, “Lie Algebras of Heat Operators in a Nonholonomic Frame”, Math. Notes, 108:1 (2020), 15–28  mathnet  crossref  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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