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Funktsional'nyi Analiz i ego Prilozheniya, 2017, Volume 51, Issue 1, Pages 4–27
DOI: https://doi.org/10.4213/faa3260
(Mi faa3260)
 

This article is cited in 10 scientific papers (total in 10 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
References:
Abstract: We construct Lie algebras of vector fields on universal bundles of symmetric squares of hyperelliptic curves of genus $g=1,2,\dots$. 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 $L_{2q}$, $q=-1, 0, 1, 2, \dots$, 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.
Received: 20.10.2016
Accepted: 20.10.2016
English version:
Functional Analysis and Its Applications, 2017, Volume 51, Issue 1, Pages 2–21
DOI: https://doi.org/10.1007/s10688-017-0164-5
Bibliographic databases:
Document Type: Article
UDC: 512.554.32+517
Language: Russian
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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\pages 4--27
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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