Some remarks about Mishchenko-Fomenko subalgebras

We discuss and compare two different approaches to the notion of Mishchenko-Fomenko subalgebras in Poisson-Lie algebras of finite-dimensional Lie algebras. One of them, commonly accepted by the algebraic community, uses polynomial Ad⁎-invariants. The other is based on formal Ad⁎-invariants and allows one to deal with arbitrary Lie algebras, not necessarily algebraic. In this sense, the latter is more universal.