Talk:Indefinite orthogonal group
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[edit] Name of this page
I've come to feel that Generalized orthogonal group is a bad name for this page. It gives the impression that the group O(p,q) is not actually a orthogonal group but some generalization thereof. What is meant, of course, is that it is a generalization of the classical orthogonal group O(n) preserving a positive-definite quadratic form on Rn. Perhaps orthogonal group (indefinite signature) would be a better name. Comments or suggestions? -- Fropuff 17:35, 7 March 2006 (UTC)
- What name is used for these groups in the literature? Pierreback 18:43, 8 March 2006 (UTC)
They are usually just referred to as "orthogonal groups", the same as O(n). To distinguish from O(n) they are sometimes called "noncompact orthogonal groups" (although O(n,C) is also noncompact) or "orthogonal groups with indefinite signature". -- Fropuff 19:18, 8 March 2006 (UTC)
Perhaps "indefinite orthogonal groups" is the best name for these groups? A search at www.ams.org/mathscinet gives three relevant hits with articles by e.g. A. Knapp and Peter Trapa. Pierreback 23:26, 24 April 2006 (UTC)
The name "indefinite orthogonal group" is also used in Wolf: Spaces of constant curvature p. 335. This book also have some interesting statements about these groups. Pierreback 23:32, 16 May 2006 (UTC)
[edit] Title needs to be changed
In representation theory groups and generally throughout Lie theory, these groups are definitely called "indefinite orthogonal groups" (sorry for the pun!). "Noncompact orthogonal groups" is descriptive, but hardly, if ever, used. I would have changed the title here and now, but it appears that one needs administrative priviledges to do it. Is this correct? Arcfrk 12:29, 10 March 2007 (UTC)
