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:
“God is a being of transcendent and unlimited perfections: his nature therefore is incomprehensible to finite spirits.”
—George Berkeley (1685–1753)
“The foolish fears of what might happen.
I cast them all away
Among the clover-scented grass,
Among the new-mown hay,
Among the husking of the corn,
Where drowsy poppies nod
Where ill thoughts die and good are born—
Out in the fields with God.”
—Elizabeth Barrett Browning (1806–1861)