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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
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.
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
Linking options:
https://www.mathnet.ru/eng/faa3260https://doi.org/10.4213/faa3260 https://www.mathnet.ru/eng/faa/v51/i1/p4
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