On the orbits in the Lie algebras of some (pseudo) orthogonal groups
type: Item
instance of: scholarly article
title: On the orbits in the Lie algebras of some (pseudo) orthogonal groups
zbMATH Open document ID: 0643.22008
author: B. George
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 4047982
zbMATH Keywords: algebraic invariants on orbits
zbMATH Keywords: Lorentz group
zbMATH Keywords: Lie algebras
zbMATH Keywords: orthogonal groups
zbMATH Keywords: de Sitter pseudo-orthogonal groups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4047982