# Can $\mathrm{PGL}_2$ be viewed as an affine algebraic group?

I was just wondering whether or not it is possible to view $\mathrm{PGL}_2$ as an affine algebraic group.

#### Solutions Collecting From Web of "Can $\mathrm{PGL}_2$ be viewed as an affine algebraic group?"

Yes, $PGL(V)$ is a linear (affine) algebra group. For more on this you can see these notes:

https://www.ma.utexas.edu/users/allcock/lag/lag14.pdf

See Theorem 7.1. Remember that $PGL(V)$ is defined as a quotient $GL(V) / \mathbb{G}_m$.