17 Jul
2003
17 Jul
'03
2:14 a.m.
Harold (mcintosh@servidor.unam.mx ) writes: << An interesting intersection of these two trains of thought is the fact that the Lie Algebra of O4 is the direct product of the Lie Algebras of two O3 rotation groups
And the rotation group SO(4) = S^3 x S^3 / (g,h) ~ (-g,-h) (where S^3 is the group of unit quaternions). Who would've thought that the rotation group SO(4) of something so round as the 3-sphere would be practically "square" (and its Lie algebra exactly square)? There's a very nice discussion of this in the Thurston notes on 3D geometry & topology that were sold by MSRI before the corresponding book got published. I'm not sure whether this discussion is in the book, too. --Dan