Time

May 29 2012 - 2:30pm - 3:18 pm

Location

CH 240

Speaker

Alexandre Turull (University of Florida)

Abstract

While the concept of isomorphism or equivalence between two individual representations of the same finite group is agreed upon and understood, it is harder to usefully describe an equivalence between collections of representations of one finite group and collections of representations of a different finite group.  One way to define these is through endoisomorphisms.  We will briefly discuss the definition of endoisomorphism.  We will note why the definition's general setting makes it particularly convenient to describe simultaneously modules in various characteristics, and the relationships among them.  We will describe how the existence of an endoisomorphism has strong consequences for the blocks of the group involved.  Endoisomorphisms may be initially defined for modules over principal ideal domains, and from these modules modules over fields in characteristic zero and modules over fields in positive characteristic can be constructed.  Under certain hypotheses, an endoisomorphism will give rise to module correspondences which preserve blocks, decomposition numbers, projective indecomposable modules, and other aspects of block theory of finite groups.