Email this article Construction of polynomials in bi-involution for singular elements of the dual space of a Lie algebra
- Authors: Lobzin F.I.1,2
-
Affiliations:
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
- Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
- Issue: Vol 216, No 10 (2025)
- Pages: 62-76
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/331246
- DOI: https://doi.org/10.4213/sm10216
- ID: 331246
Cite item
Open Access
Access granted
Subscription Access
Abstract
A generalization of the well-known problem of he construction of complete full bi-involutive sets of polynomials on the conjugate space of a Lie algebra to the case of singular covectors is considered. A generalization of the Mishchenko–Fomenko method of argument shift to the case of singular covectors if proposed and sufficient conditions for the completeness of the resulting sets are found. Using this method, it is shown that complete bi-involutive sets of polynomials can be constructed for singular covectors in all reductive Lie algebras.
About the authors
Feodor Igorevich Lobzin
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia; Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
Email: fiadat@mail.ru
References
- A. V. Bolsinov, P. Zhang, “Jordan–Kronecker invariants of finite-dimensional Lie algebras”, Transform. Groups, 21:1 (2016), 51–86
- A. Bolsinov, V. S. Matveev, E. Miranda, S. Tabachnikov, “Open problems, questions and challenges in finite-dimensional integrable systems”, Philos. Trans. Roy. Soc. A, 376:2131 (2018), 20170430, 40 pp.
- J.-Y. Charbonnel, A. Moreau, “The index of centralizers of elements of reductive Lie algebras”, Doc. Math., 15 (2010), 387–421
Supplementary files
