On abstract homomorphisms of algebraic groups

Pralay Chatterjee

Published 2015-11-19Version 1

In this paper we study abstract group homomorphisms from the groups of rational points of linear algebraic groups which are not necessarily reductive. One of our main goal is to obtain results on homomorphisms from the groups of rational points of linear algebraic groups defined over certain specific fields to the groups rational points of linear algebraic groups over finite extensions of $\Q$ and $\q$. We also obtain results on abstract homomorphisms from unipotent and solvable groups, and prove results on the structures of abstract homomorphisms using the celebrated results of Borel and Tits on abstract homomorphisms of algebraic groups and results due to Tits on the structure of the groups of rational points of isotropic semisimple groups