Thursday, July 19th, 2012 | Author: Konrad Voelkel
If you don't have a solid education in linear algebraic groups, you might nevertheless encounter the term "reductive groups" now and then. People keep telling you to think about , as an algebraic group, and that's a good first approximation. If you want to go a step further, some confusion can happen, since the definition of reductive groups can be given for groups over the complex numbers in two quite different ways and only one of them generalizes to reductive groups over other fields, and if one wants to do non-perfect fields, it gets even more complicated.
I want to give some very short explanations on how to think about reductive groups and semisimple algebraic groups.