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)
“I was in love with a beautiful blonde once. She drove me to drink. That’s the one thing I’m indebted to her for.”
—Otis Criblecoblis, U.S. screenwriter. W.C. Fields (W.C. Fields)