Speaker:  Alexandra Garazha (MSU, Moscow)

Date and time:  31.01.2024, 17:00 (GMT +03:00)

Title: Kronecker's method and complete systems of functions in bi-involution on classical Lie algebras

Abstract: We examine the relation of the integrability property and the bi-Hamiltonian structure, the latter means that there are two compatible Poisson brackets and the dynamics is Hamiltonian with respect to both of them. We study the simplest case when one bracket is linear and the other one is constant. Namely, we will consider a classical simple Lie algebra g and define two Poisson brackets: the classical Lie-Poisson bracket and the bracket "with frozen argument A", which can be constructed for any A ∈ g. 

If A is regular, the corresponding complete systems of functions in bi-involution can be obtained by the Mishchenko-Fomenko argument shift method. We will show how to generalize this method to the case of an arbitrary element A using an algebraic approach.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com