Talk:SO(4)
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[edit] Relation to orbital mechanics
The article on the Laplace-Runge-Lenz vector has the set of commutation relations for the Lie algebra of SO(4) as they are commonly taught to physics students. These are notably absent from this article. These are important for several reasons: (1) they help emphasize that the difference between this and SO(3,1) is a change of sign, and (2) they help emphasize the decomposition of of SO(3,1) as the product of a pair of complex conjugate reps of SL(2,C). I'm not clear on what the decomposition of the adjoint rep of SO(4) is w.r.t. the fundamental rep. In particular, I'd like to see a deeper treatment of the representations of SO(4), and the homotopy groups, etc. linas 02:50, 18 June 2006 (UTC)
[edit] How can two planes intersect in a point?
"Every plane B that is completely orthogonal (*) to A intersects A in a certain point P." As far as I know planes intersect in planes, lines or not at all.
- That's true only in three dimensions. In four dimensions, planes generically intersect in points. Take for example the plane spanned by the first two coordinate vectors and the plane spanned by the last two. These two planes intersect only at the origin. -- Fropuff 16:30, 10 November 2006 (UTC)
