Acta Applicandae Mathematica

, Volume 90, Issue 1–2, pp 65–89 | Cite as

Adjoint and Coadjoint Orbits of the Poincaré Group

Original Paper


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.

Key words

adjoint orbit coadjoint orbit cotype type 

Mathematics Subject Classifications (2000)

20E45 22E15 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of UtrechtUtrechtThe Netherlands

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