Division algebras $(\mathbb{R,C,H,O})$ and discrete symmetry [closed]

I once saw a statement about the relation between division algebra(which means you can define a division in this algebra, there is a theorem saying we only have 4 kinds of division algebra, real R, complex C, quaternion H and octonion O) and discrete symmetries, saying that the number of discrete symmetries(I mean time reversal, charge conjugate and parity) is limited because we only have 3 kinds of associative division algebra(octonion O is not associative, I guess the associativity is related to physical operation, since all physical operation is associative, I mean ABC=A(BC)).

This statement seems to be very interesting and deep, however, I don't know much about this. Just want to attract you physicists attention and give some comments or explanation about this.

Thank you very much!

For more about division algebra:

http://en.wikipedia.org/wiki/Division_algebra#Associative_division_algebras

http://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(normed_division_algebras)#Hurwitz.27s_theorem

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closed as off topic by Qmechanic♦, Manishearth♦, Sklivvz♦Dec 27 '12 at 16:36

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