Adjoint and coadjoint orbits of the Poincaré group

Details Adjoint and coadjoint orbits of the Poincaré group Adjoint and coadjoint orbits of the Poincaré group

2003-05-30

arxiv.org/abs/math/0305442v2

Acta Appl Math 90 (2006) 65-89

Mathematics

Representation Theory

42 pages; final version

Scientific paper

10.1007/s10440-006-9031-8

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.

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