Finite Fields
When working over finite fields, one defines a "reflection" as a map that fixes a hyperplane (otherwise for example there would be no reflections in characteristic 2, as so reflections are the identity). Geometrically, this amounts to including shears in a hyperplane. Reflection groups over finite fields of characteristic not 2 were classified in (Zalesskiĭ & Serežkin 1981).
Read more about this topic: Reflection Group
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“The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.”
—Blaise Pascal (1623–1662)
“Genius is the naturalist or geographer of the supersensible regions, and draws their map; and, by acquainting us with new fields of activity, cools our affection for the old. These are at once accepted as the reality, of which the world we have conversed with is the show.”
—Ralph Waldo Emerson (1803–1882)