Basics of reductivity and semisimplicity. Math 249B. Basics of reductivity and semisimplicity In the previous course, we have proved the important fact that over any eld k, a non-solvable …

Reductive elimination, the reverse of oxidative addition, is most often seen in higher oxidation states because the formal oxidation state of the metal is reduced by two units in the reaction.

These notes are a guide to algebraic groups, especially reductive groups, over a field. Proofs are usually omitted or only sketched. The only prerequisite is a basic knowledge of commutative …

Given a split reductive group, deriving its root datum is relatively straightforward. I want to sketch here how for any field F the group G(F) is constructed from a datum.

Joe Harris taught a course (Math 224) on representations of reductive Lie groups at Harvard in Spring 2013. These are my \live-TEXed" notes from the course. Conventions are as follows: …

In study of the reductive group GL(n; C), the subgroup GL(1; C)n = (C )n plays an important part. Reason is that almost every element of GL(n; C) is conjugate to an element of GL(1; C)n.

Defining Reductive Let k be an algebraically closed field. Reductive algebraic groups over k include some familiar groups: