Department of Mathematics
"Classifiying the simple functors of the bifree monomial Burnside category"
İSMAİL ALPEREN ÖĞÜT
Abstract: In the study of FG-modules for a prime-characteristic field F and a finite group G, an important role is played by the twisted permutation FG-modules, we mean, the direct sums of those FG-modules that are induced from 1-dimensional modules. These modules come from F-twisted G-sets. We shall introduce a category, the bifree monomial Burnside category, whose objects are finite groups and whose morphisms to G from H are spanned by those F-twisted G-H-bisets such that the left G-action and right H-action are free. We shall classify the simple functors from this category to the category of vector spaces over a given sufficiently large characteristic-zero field. The motive is that our category is a toy version of a similar category, the bifree trivial source category, which Robert Boltje and Philipp Perepelitsky have recently used to investigate invariants under a new notion of equivalence for blocks of group algebras over F.
Date: Monday, April 25, 2016
Place: Mathematics Seminar Room, SA-141
All are most cordially invited. Tea and cookies will be served after the talk.