Timeline for About reflections of reflection groups
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| Mar 21, 2017 at 9:29 | comment | added | wendy.krieger | You must understand that a hyperplane is space itself. Coxeter himself describes groups where there are order-three reflections etc, such as the group 3(3)3 => AAA = BBB = 1, ABA = BAB. Likewise, the intersection of two planes is an orthohedrix, the space orthogonal to a hedrix or 2-space. You will note then that (AB)^n constitutes a rotation. | |
| Mar 19, 2017 at 16:17 | comment | added | Jim Humphreys | In the Bourbaki definition of "Coxeter group" (inspired mainly by work of Tits), a "reflection" always fixes a hyperplane, so your first sentence doesn't apply. For example, the identity element is not a "reflection". | |
| Dec 21, 2016 at 13:54 | history | answered | wendy.krieger | CC BY-SA 3.0 |