Seminar (online) 15.11.2023: Ivan Kozlov
Title: Jordan-Kronecker invariants and Integrable Hamiltonian systems
Abstract:
The Jordan-Kronecker invariants of a complex finite-dimensional Lie algebra were introduced by A.V. Bolsinov and P. Zhang in [1]. In short, they are the canonical form of a pencil of skew-symmetric bilinear forms.
In the talk we will discuss the latest results about the Jordan-Kronecker invariants and their relation with the integrability of Hamiltonian systems. In particular, we will talk about the new results from [2] and [3].
[1] A.V. Bolsinov and P. Zhang “Jordan-Kronecker invariants of finite-dimensional Lie algebras”, Transformation Groups, 21:1 (2016), 51–86
[2] I.K. Kozlov “Realization of Jordan-Kronecker invariants by Lie algebras”, arXiv:2307.08642 [math.DG]
[3] I.K. Kozlov “Shifts of semi-invariants and complete commutative subalgebras in polynomial Poisson algebras”, arXiv:2307.10418 [math.RT]