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
Famous quotes containing the words finite and/or fields:
“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)
“The world’s great day is growing late,
Yet strange these fields that we have planted
So long with crops of love and hate.”
—Edwin Muir (1887–1959)