Some remarks about Mishchenko-Fomenko subalgebras

We discuss and compare two different approaches to the notionof Mishchenko–Fomenko subalgebras in Poisson–Lie algebras of finite-dimensional Lie algebras. One of them, com-monly 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 neces-sarily algebraic. In this sense, the latter is more universal.