[racket] SU(2) and friends

Many thanks for the continuing interest. 

As you say, the 2nd is closer to my level and more accessible to me.
(The first is likely to take me rather longer to be able to tackle.)

Something  I came across in the late Pertti Lounesto's "Clifford
Algebras and Spinors" (2e, 2001; ISBN 0-521-00551-5), which resembles
your 2nd ref,  makes statements such as: 

"In general, a rotation in R^4 has two invariant planes which are
completely orthogonal, in particular they have only one point in
common." ( p. 83)

and 

"There are three different kinds of rotations in four dimensions..." (p.
89).  

Do you think there are any references to spaces of two complex
dimensions that make statements of this sort? Or maybe I should be
working them out for myself.

 

-----Original Message-----
From: Gregory Woodhouse [mailto:gregwoodhouse at me.com] 
Sent: 22 April 2011 18:23
To: Paul Ellis
Cc: users at racket-lang.org
Subject: SU(2) and friends

I meant to get back to this earlier.  You might want to look at

Geometry of Representation Spaces in SU(2) - advanced, but with some
real gems
http://arxiv.org/pdf/1001.2408

The Quaternions and the Spaces S3, SU(2), SO(3), and RP3
http://www.cis.upenn.edu/~cis610/cis610sl7.pdf

The first of these is fairly advanced, but if you have a background in
differential geometry, it's well worth reading. The second is more
accessible, using explicit matrix manipulations and such.

Oh, and don't forget Wolfram Mathworld! It's a very useful online
encyclopedia of mathematics.

http://mathworld.wolfram.com/SpecialUnitaryGroup.html

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