Let $G$ be a simply connected semisimple algebraic $K$-group and $K$ be a finite extension of $k$. Is $R_{K/k}G$ still a simply connected algebraic group?

We say $G$ is simply connected if for any central isogeny $G'\to G$ is in fact an isomorphism of algebraic groups.

`$G$`

. In any case it's important to indicate whether you need any extra assumptions about the fields or the field extension involved. – Jim Humphreys Feb 26 '11 at 13:19`$\mathbb{C}$`

with the topological characterization. The notion comes up in many books and papers, such as the papers by Borel-Tits on reductive groups available at NUMDAM numdam.org:80/?lang=en. Or see 31.1 in my 1975 Springer GTM21 on linear algebraic groups. Some of the standard online reference sources are not too helpful here. – Jim Humphreys Feb 26 '11 at 14:44