"Almost linear functional on Lie algebras"
Assume you have a real-valued functional on a real Lie algebra whose restriction to any abelian subalgebra is linear. Does this functional have to be linear? If not, to which extent is such a non-linear functional unique? I will discuss how these questions are related to a mathematical model of quantum mechanics, symplectic topology and the structure of classical Lie algebras.
The talk is based on joint works with Leonid Polterovich.