Let G be a Lie group or algebraic group. G is called reductive over a field k if every representation of G over k is completely reducible

For example, a finite groupMathworldPlanetmath is reductive over a field k if and only if its order is not divisible by the characteristic of k (by Maschke’s theorem). A complex Lie group is reductive if and only if it is a direct productMathworldPlanetmathPlanetmathPlanetmathPlanetmath of a semisimple group and an algebraic torus.

Title reductive
Canonical name Reductive
Date of creation 2013-03-22 13:23:49
Last modified on 2013-03-22 13:23:49
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 6
Author bwebste (988)
Entry type Definition
Classification msc 22C05