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:
“All finite things reveal infinitude:”
—Theodore Roethke (1908–1963)
“As the fields fear drought in autumn, so people fear poverty in old age.”
—Chinese proverb.