What are the classical compact connected lie groups?

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I think they are $SO(n),SU(n),Sp(n)$, and $Spin(n)$ but I'm not sure. Any help would be appreciated.

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They are groups $SO(n),Sp(n),SU(n),U(n)$. At least usually these are called "classical". If you are interested in simple ones, you get $SO(n),Sp(n),SU(n)$.