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This is only a minor question.
I watched an on-line video recently on su2 and how it applies to Physics. Now, one of the first things the instructor did was to change the base to sl2. Fine and all, but she called sl2 "su2" for the whole video. Since the two Lie algebras have different structure factors how can she do this? Or was she just being a Physicist and sloppy about it?
Another example. My text is talking about the Cartan-Weyl basis of sl3, then changes the basis to a Chevalley basis. The problem here is not merely that the structure factors are different but now the simply laced root system for the Cartan basis is no longer simply laced in the Chevalley basis. And yet the text still refers to it as sl3.
What gives?
-Dan
I watched an on-line video recently on su2 and how it applies to Physics. Now, one of the first things the instructor did was to change the base to sl2. Fine and all, but she called sl2 "su2" for the whole video. Since the two Lie algebras have different structure factors how can she do this? Or was she just being a Physicist and sloppy about it?
Another example. My text is talking about the Cartan-Weyl basis of sl3, then changes the basis to a Chevalley basis. The problem here is not merely that the structure factors are different but now the simply laced root system for the Cartan basis is no longer simply laced in the Chevalley basis. And yet the text still refers to it as sl3.
What gives?
-Dan