I need HELP with group algebras and finite dimensional ideals

From: Warren065 (warren065_at_aol.com)
Date: 01/29/05 

Date: 29 Jan 2005 21:24:18 GMT

First a definition: Let G be any group (multiplicative) and let F be any
field. The F-algebra with G as a basis wand with multiplication defined by
extending the original group multiplication on G to the whole algebra. This
F-algebra denoted FG is the group algebra of G over F.

The problem: Show that the group algebra FG contains a finite-dimensional
ideal IFF G is finite. Also, show that if G is finite, then there is a
1-dimensional ideal.

I think that my linear algebra background is lacking. I can't even get started
on this.

Warren

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