Speaker: Baptiste Rognerud (Amiens)
Title: Equivalences Between Blocks of Mackey Algebras
Abstract: Let \(G\) be a finite group and \(k\) a field of characteristic \(p > 0\). There are lots of similarities between the category of modules over the group algebra and the category of modules over the Mackey algebra (i.e., the category of Mackey functors). In particular there is a bijection between the blocks of \(kG\) and the blocks of the so called \(p\)-local Mackey algebra.
In this talk we give some evidences and some answers to the following question:
Let \(G\) be a finite group and \(b\) be a block of \(kG\) with abelian defect group \(D\). Let \(b'\) be the Brauer correspondent of \(b\) in \(N_{G}(D)\). Is there a derived equivalence between the corresponding blocks of the \(p\)-local Mackey algebra?
