Richard Cushman, Wilberd van der Kallen
Published 2003-05-30, updated 2016-04-07Version 3
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 Poincar\'{e} group.
Comments: Revised arguments in section 6, results unchanged
Journal: Acta Appl Math 90 (2006) 65-89
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