Abstract
In the present paper, Lie groups with the multivalued Casimir functions are examined, in particular, a definition of the multivalued Casimir functions is given. It is demonstrated that when a Lie group consists of the essentially multivalued Casimir functions, the space of orbits of the coadjoint representation is non–semi-Hausdorff one, which allows a criterion for identification of these groups to be formulated. As an example, complete involute sets of the Casimir functions are retrieved for all real five-dimensional Lie algebras, and two Lie algebras with a non-Hausdorff space of orbits are identified by this criterion.
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