Adjoint and Coadjoint Orbits of the Poincaré Group |
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Authors: | Richard Cushman Wilberd van der Kallen |
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Institution: | (1) Mathematics Institute, University of Utrecht, 3508TA Utrecht, The Netherlands |
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Abstract: | In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we classify the adjoint and coadjoint orbits of the Poincaré group.The author (R.C) was partially supported by European Community funding for the Research and Training Network MASIE (HPRN-CT-2000-00113). |
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Keywords: | adjoint orbit coadjoint orbit cotype type |
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