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Right now I'm using "Affine Lie Algebras and Quantum Groups" by Fuchs. I'm getting sick of it. As a Physicist the structure and focus of the text is attractive to me. But, to give one example...
The text constructs two vector spaces: L and Lw. Lw is dual to L. The text goes on to state that \(\displaystyle L \subset Lw\). As the two spaces are dual this cannot be.
BUT: The next paragraph shows how to interpret this. We can (apparently) define a metric between the two spaces and if we use the metric to compare the space dual to L to Lw then we find that L is a subspace of Lw which given the definitions of both spaces is a completely banal comment and isn't actually needed.
I can't take this kind of presentation any more!
Does anyone know of a decent Lie algebra text? I would appreciate with a Physics bent, but that isn't necessary.
Thanks!
-Dan
The text constructs two vector spaces: L and Lw. Lw is dual to L. The text goes on to state that \(\displaystyle L \subset Lw\). As the two spaces are dual this cannot be.
BUT: The next paragraph shows how to interpret this. We can (apparently) define a metric between the two spaces and if we use the metric to compare the space dual to L to Lw then we find that L is a subspace of Lw which given the definitions of both spaces is a completely banal comment and isn't actually needed.
I can't take this kind of presentation any more!
Does anyone know of a decent Lie algebra text? I would appreciate with a Physics bent, but that isn't necessary.
Thanks!
-Dan