Classical Lie groups

In the language of linear algebraic groups, the connected classical groups are the connected reductive groups of Dynkin types${\displaystyle A_{n}}$, ${\displaystyle B_{n}}$, ${\displaystyle C_{n}}$, and ${\displaystyle D_{n}}$, together with their forms over arbitrary fields. Over ${\displaystyle \mathbb {R} }$ and ${\displaystyle \mathbb {C} }$ this recovers the familiar classical Lie groups, while over finite fields one obtains the finite classical groups.