Algebraic method for construction of infinitesimal invariants of Lie groups representations

Abstract

We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation space, which allows us to regard it as a coalgebra of some Lie algebra. In its turn, this allows us to reduce the problem of constructing invariants of a given representation to the problem of constructing invariants of the coadjoint representation of the corresponding Lie group. In our previous paper it was shown that this problem can always be solved in a natural way by the methods of linear algebra.