Some remarks about Mishchenko-Fomenko subalgebras

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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 -invariants. The other is based on formal -invariants and allows one to deal with arbitrary Lie algebras, not necessarily algebraic. In this sense, the latter is more universal.