Let V a vector space over some field K (usually K= or K=). Let G be a group which acts on V. This means that there is an operationMathworldPlanetmath ψ:G×VV such that

  1. 1.


  2. 2.


  3. 3.


where gv stands for ψ(g,v) and e is the identity elementMathworldPlanetmath of G.

If in addition,


for any gG, v,wV, c,dK, we say that V is a G-module. This is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath with the existence of a group representationMathworldPlanetmathPlanetmath from G to GL(V).

Title G-module
Canonical name Gmodule
Date of creation 2013-03-22 14:57:53
Last modified on 2013-03-22 14:57:53
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 6
Author rspuzio (6075)
Entry type Definition
Classification msc 20C99
Related topic GroupRepresentation
Related topic Group