Recent content by dg0666

In characteristic zero any linear representation of a reductive group is semisimple. Also in characteristic zero any linear representation of a finite group is semisimple (Maschke's Thm). However is any linear representation of any group semisimple in characteristic zero?

Great. I think that has answered my question very well. My confusion arosed because of a misunderstanding between isomorphisms and continuous maps but thanks very much for your help. Dan

In fact I understand that distinction. What is confusing me is that the affine varieties are closed in one topology and they are mapped isomorphically onto open subsets in P^n. It is just this bijection between open and closed subsets which is confusing me. Should I be confused by this or is...

The book I am reading, Linear Algebraic Groups by Humphreys defines a prevariety X in projective space P^n to be a noetherian topological space endowed with a sheaf of functions such that X is the union of finitely many open subsets, each isomorphic to an affine variety. This confuses me...