Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Modules & Representations

  1. Aug 30, 2011 #1
    There is a Theorem that says FG-Modules are equivalent to group representations:

    "(1) If [itex]\rho[/itex] is a representation of G over F and V = [itex]F^{n}[/itex], then V becomes an FG-Module if we define multiplication vg by: vg = v(g[itex]\rho[/itex]), for all v in V, g in G.

    (2) If V is an FG-Module and B a basis of V, then [itex]\rho[/itex]: g [itex]\mapsto[/itex] [itex][g]_{B}[/itex] is a representation of G over F, for all g in G"

    I've been told and I have read that using FG-Modules is advantageous to using group representations, but what exactly is the advantage of this, other than getting results like Maschke's Theorem?!

    Thanks for any help!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?