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**Summary::**Where can I find further discussion of the algebra(s) of “basic reflections” (e.g. γ^2 = -1 ), mentioned in Sec. 11.5 of Penrose’s "Road to Reality"?

In Roger Penrose’s Chapter 11 of

*Road to Reality*, titled ‘Hypercomplex Numbers’, he discusses Clifford Algebra elements being constructed out of “basic reflections” γ (gamma) or “first order (‘primary’) entities” in terms of “quaternion-like relations” among these basic reflections, such as γ(i)^2 = -1 etc.

While I’m familiar with the construction of rotations out of reflections, none of my other references on Clifford Algebras or reflection groups (e.g. Pertti Lounesto's

*Clifford Algebras and Spinors*, or works by Coxeter), seem to refer specifically to an algebra of reflections, or identify them as directly constituting any of the simplest Clifford Algebras.

I'm particularly interested to find a visualisable geometric/diagrammatic view of how reflections can act spinorially, such that γ(i)^2 = -1.

Where can I find more about this algebra of basic reflections, if indeed there is anything more to them than Penrose states (relevant pages, 208-211, attached)?

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