nLab
classical Lie group

The classification of simple Lie groups contains four infinite series of “classical” simple Lie groups:

• $A_n=\mathrm{SU}(n+1)$, the special unitary group

• $B_n=\mathrm{SO}(2n+1)$, the special orthogonal group

• $C_n=\mathrm{Sp}(n)$, the symplectic group

• $D_n=\mathrm{SO}(2n)$, the special orthogonal group

Apart from this there are five exceptional Lie groups.

More generally, other matrix Lie groups, such as the general linear group $\mathrm{GL}(n)$, may be called “classical”.