How does the classification of semisimple lie algebras actually work? If it's all based on the cartan subalgebra, aren't we omitting all the information about all the generators not in the cartan subalgebra? If someone can give me a hand-wavey explanation I'd be very greatful.
>>16547580It's a method for mapping dimensional expansion without calling it dimensional expansion because standard model physicists don't know what dimensions are which is why the do unit analysis.
>>16547580>aren't we omitting all the information about all the generators not in the cartan subalgebraThe Chevalley-Serre relations link the rest of the generators to the Cartan subalgebra via the Cartan matrix. This is why you can just look at a Dynkin diagram and tell the entire bracket structure from it alone.
