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I've tried to answer this question, but I need some help.

What is the possible dimension of irreducible representations of Abelian Lie Algebras? I think it is always one, but I am not sure.

Thank you.

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Try to formulate what a representations of an Abelian Lie Algebra is precisely. And what it maens for it to be irreducible. – Marc van Leeuwen Nov 15 '12 at 17:16

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