Re: Why is there no *really* useful Algebra beyond complex numbers?

Here's a book with relevance to physics:

Dixon, G. M. Division Algebras: Octonions, Quaternions, Complex Numbers
and the Algebraic Design of Physics. Dordrecht, Netherlands: Kluwer,
1994.

Here are two papers on the proof of the theorem that the reals, complex
numbers, quaternions, and octonions are the only real finite
dimensional division algebras:

Adams, J. F. "On the Non-Existence of Elements of Hopf Invariant One."
Ann. of Math. 72, 20-104, 1960.

Bott, R. and Milnor, J. "On the Parallelizability of the Spheres."
Bull. Amer. Math. Soc. 64, 87-89, 1958

.

Relevant Pages

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