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

This article is cited in 4 scientific papers (total in 4 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

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English version:
Functional Analysis and Its Applications, 2017, 51:1, 2–21

Bibliographic databases:

Document Type: Article
UDC: 512.554.32+517
Received: 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. Bunkova E.Yu., “Differentiation of Genus 3 Hyperelliptic Functions”, Eur. J. Math., 4:1, 1, SI (2018), 93–112  crossref  mathscinet  zmath  isi  scopus
    4. O. K. Sheinman, “Integriruemye sistemy algebraicheskogo proiskhozhdeniya i razdelenie peremennykh”, Funkts. analiz i ego pril., 52:4 (2018), 94–98  mathnet  crossref  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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