On the orbits in the Lie algebras of some (pseudo) orthogonal groups (Q1101837)

The authors give a complete classification of the orbits in the Lie algebras of the groups SO(N), \(n=3,4,5\), and of the groups \(SO_ 0(n,1)\), \(n=2,3,4\), SO(n,2), \(n=2,3\). The classification is carried out by making use of elementary geometrical methods, exhibiting the relevance of the results for a lower dimensional group in obtaining the results for a higher dimensional one. For each orbit the values of the algebraic invariants are calculated. For the orthogonal groups the orbit structure is relatively simple. For the Lorentz and the de Sitter pseudo-orthogonal groups it becomes progressively complex. The orbits are classified and tabulated in a form that makes it easy for applications.