Lie(G2) representations

I've been dabbling octonians and related Lie algebras, trying to get a
feel for how they work. I've come up with what I think is an elegant
representation for the exceptional Lie group G2, that I haven't seen
elsewhere. Mostly I'm generalizing from the paper "Euler Angles for
G2" by Cerchiai, et. al.

I've written up what I have so far.
<http://www.megaseattle.com/james/Geometry/Understanding_G2.pdf>
(240K)

Is there someone (who knows more about this stuff that I do) who would
be willing to look it over and give me some feedback? I'm a Physicist
by training, but I don't have any academic connections right now.

Many thanks,
James

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