Wronskians as N-ary brackets in finite-dimensional analogues of sl(2)

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Abstract

The Wronskian determinants (for coefficients of higher-order differential operators on the affine real line or circle) satisfy the table of Jacobi-type quadratic identities for strong homotopy Lie algebras - i.e. for a particular case of L∞-deformations - for the Lie algebra of vector fields on that one-dimensional affine manifold. We show that thestandard realisation of sl(2) by quadratic-coefficient vector fields is the bottom structurein a sequence of finite-dimensional polynomial algebras KN[x] with the Wronskians as N-ary brackets; the structure constants are calculated explicitly.

Original languageEnglish
Title of host publication29th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2025
Editors C. Burdik
PublisherInstitute of Physics
Number of pages8
DOIs
Publication statusPublished - 2025
Event29th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2025 - Prague, Czech Republic
Duration: 7-Jul-202511-Jul-2025

Publication series

NameJournal of Physics: Conference Series
PublisherIoP Publishing
ISSN (Print)1742-6588
ISSN (Electronic)3152

Conference

Conference29th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2025
Country/TerritoryCzech Republic
CityPrague
Period07/07/202511/07/2025

Keywords

  • L∞-algebra
  • N-ary bracket
  • sl(2)
  • strong homotopy Lie algebra
  • Vandermonde determinant.
  • Witt algebra
  • Wronskian determinant

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