Generalized Casimir operators of solvable Lie algebras with Abelian nilradicals

A solvable complex Lie algebra L, of dimension N, with an Abelian nilradical of dimension r is shown to have precisely 2r-N generalized Casimir invariants (we always have r>or=N/2). They are constructed as invariants of the coadjoint representation of L and depend only on variables dual to elements of the nilradical. Their form, in general, involves logarithms of these variables in addition to rational and irrational functions. They give rise to genuine Casimir operators whenever they happen to be polynomials.

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