Lie Group

A Lie group is a group with smooth structure.

A Lie group is a smooth manifold whose underlying set of elements is equipped with the structure of a group such that the group multiplication and inverse-assigning functions are smooth functions

Classical Lie Groups

The classical examples for Lie groups are

• General linear $\mathrm{GL}(n)$
• Special linear $\mathrm{SL}(n)$
• Orthogonal $\mathrm{O}(n)$
• Special orthogonal $\mathrm{SO}(n)$
• Unitary $\mathrm{U}(n)$
• Special Unitary $\mathrm{SU}(n)$
• Symplectic $\mathrm{Sp}(\mathrm{n})$\