TITLE: Automorphisms of $SL_n$ as a variety
QUESTION [9 upvotes]: What are the automorphisms of $SL_n$ as an algebraic variety?
In other words, let $k$ be an algebraically closed field of characteristic 0 (e.g., $k=\mathbb{C}$). Let $\tau$ be an automorphism of $SL_n$ regarded as an algebraic variety over $k$. Assume that $\tau$ takes the unit element $e$ of $G$ to itself. Is it true that $\tau$ is an automorphism of $SL_n$ as an algebraic group over $k$?

REPLY [9 votes]: The automorphism group is massive!  
Flexible varieties and automorphism groups, 
I. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, M. Zaidenberg, http://arxiv.org/abs/1011.5375.