Robin Cockett

Date: November 22, 2023
Time: 11:00 am - 12:00 pm
Location: ICT 616

Title: A categorical introduction to Drazin inverses

Abstract: Michael Drazin introduced the idea of a “pseudoinverse” for rings and semigroups in 1961.  These inverses categorically are rather special as (like ordinary inverses) they are preserved by all functors when they exist.   A category is Drazin when all maps have a Drazin inverse.  The aim of the talk is prove that when a category has “expressive” rank it must be Drazin.  This provides some examples of Drazin categories  … time permitting I will explain how Drazin inverses relate to the Fitting decomposition and the Jordan -Chevalley decomposition.