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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
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