Expressing the punctured affine plane as a quotient.

Question

In this paper Toen states (on p.50) that the punctured affine plane $\mathbb{A}^{n}\backslash\{0\}$ is equivalent (as a stack) to a quotient stack $[\mathrm{sl}_{2}/\mathbb{G}_{a}]$. It is not even clear to me what the $\mathbb{G}_{a}$-action on $\mathrm{sl}_{2}$ could be. Can anyone offer any hints about how to prove this?

Answer 1

$SL_2$ acts transitively on $\mathbb{A}^2 \setminus \{0\}$ and the stabilizer of the point $(1,0) \in \mathbb{A}^2$ is the subgroup $$ \begin{pmatrix} 1 & t \\ 0 & 1 \end{pmatrix} \cong \mathbb{G}_a. $$ Consequently, $\mathbb{A}^2 \setminus \{0\} \cong SL_2/\mathbb{G}_a$.