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If one generator of a Lie algebra commutes with all other generator,then why must this generator be the generator of U(1) trasformation?(I know that generator of U(1) commutes with all other generators).

By the way,compact simple Lie algebras belong to 3 families called classical groups,with only 5 exceptions.What are the five exceptions?(QFT of Peskin and Schroeder)

Thank you very much in advance

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# If one generator commutes with all other,why must it be generator of U(1)?

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