Аннотация:We give an explicit formula for the index of a Lie algebra of the shape h⊕(g/h), where g is a semisimple Lie algebra, h is a subalgebra in g and the h-module g/h is regarded as an Abelian ideal. This formula has applications to Poisson commutative subalgebras in the symmetric algebra S(g) and to completely integrable systems.