@inproceedings{89733e0908174841a22203406359a117,
title = "Wronskians as N-ary brackets in finite-dimensional analogues of sl(2)",
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.",
keywords = "L∞-algebra, N-ary bracket, sl(2), strong homotopy Lie algebra, Vandermonde determinant., Witt algebra, Wronskian determinant",
author = "Kiselev, \{Arthemy V.\}",
note = "Publisher Copyright: {\textcopyright} Published under licence by IOP Publishing Ltd.; 29th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2025 ; Conference date: 07-07-2025 Through 11-07-2025",
year = "2025",
doi = "10.1088/1742-6596/3152/1/012044",
language = "English",
series = "Journal of Physics: Conference Series",
publisher = "Institute of Physics",
editor = "Burdik, \{ C.\}",
booktitle = "29th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2025",
}