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The entry Clifford algebra used to state the classification and Bott periodicty over the complex numbers, but not over the real numbers. I have added in now the relevant statements, straight from Lawson-Michelson:
Just the bare statements so far.
have added these two pointers:
Robert A. Wilson, A group-theorist’s perspective on symmetry groups in physics (arXiv:2009.14613)
Robert A. Wilson, On the Problem of Choosing Subgroups of Clifford Algebras for Applications in Fundamental Physics, Adv. Appl. Clifford Algebras 31, 59 (2021) (doi:10.1007/s00006-021-01160-5)
Will also add these to standard model of particle physics.
Isn’t it that from the two basis elements of $\mathbb{R}^{(2,0)}$, $e_1$ and $e_2$ squaring to $-1$, the Clifford algebra is generated by $\{1, e_1, e_2, e_1 e_2\}$, the latter three generators squaring to $-1$?
Yes. Ideally the entry would explain how the identification works. (Myself, i have no time right now, maybe later…)
I’ve rolled back to version #28.
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