# Classification of Division Algebras

Tuesday, January 27th, 2015 | Author:

I was asked to give a talk about division algebras (purpose and classification). This is a rough overview of it, mostly learned from the book of Springer and Veldkamp "Octonions, Jordan Algebras and Exceptional Groups" and the book of Lam "Noncommutative Rings". The book "Numbers" by Ebbinghaus et al. was also nice to read along for references.

We will look mostly at finite dimensional (not neccesarily associative) division algebras over the real numbers.

Instead of these rather loose notes, you may prefer to look at my texed notes in this pdf file.

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# What is ... a reductive group?

Thursday, July 19th, 2012 | Author:

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 $GL_n$, 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.

Category: English, Mathematics | 3 Comments