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Casimir Functions for Five-Dimensional Lie Groups with a Non–Semi-Hausdorff Space of Orbits

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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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Authors and Affiliations

  1. Omsk State University, Russia

    A. A. Magazev

Authors
  1. A. A. Magazev
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Magazev, A.A. Casimir Functions for Five-Dimensional Lie Groups with a Non–Semi-Hausdorff Space of Orbits. Russian Physics Journal 46, 912–920 (2003). https://doi.org/10.1023/B:RUPJ.0000015250.51876.6b

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  • DOI: https://doi.org/10.1023/B:RUPJ.0000015250.51876.6b

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