Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves

DOI10.1007/s10688-017-0164-5zbMath1425.17031OpenAlexW2594947730WikidataQ59890379 ScholiaQ59890379MaRDI QIDQ2364478

Victor M. Buchstaber, Alexander V. Mikhailov

Publication date: 21 July 2017

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: http://eprints.whiterose.ac.uk/123925/1/0002.pdf

zbMATH Keywords

commuting operatorssymmetric polynomialsinfinite-dimensional Lie algebraspolynomial dynamical systemsrepresentations of the Witt algebrasymmetric powers of curves

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Plane and space curves (14H50) Families, moduli of curves (algebraic) (14H10) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (8)

Two-valued groups, Kummer varieties, and integrable billiards ⋮ Hyperelliptic sigma functions and Adler-Moser polynomials ⋮ The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications ⋮ Lie algebras of heat operators in a nonholonomic frame ⋮ Almost graded current algebras on the symmetric square of a curve ⋮ Polynomial Hamiltonian integrable systems on symmetric powers of plane curves ⋮ Differentiation of genus 3 hyperelliptic functions ⋮ On the problem of differentiation of hyperelliptic functions

Cites Work

• Polynomial dynamical systems and the Korteweg-de Vries equation
• Algebraic constructions in the category of Lie algebroids
• Commuting families in skew fields and quantization of Beauville's fibration
• Polynomial Lie algebras
• Wave front evolution and equivariant Morse lemma
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