Speaker:  Laurence John Barker (Bilkent University)

Title:  The Puig category of a block and conjectural isomorphism invariance of the multiplicities of the objects

Abstract: A modular group algebra decomposes as a sum of algebras called block algebras. The group acts as automorphisms on each block algebra. Reducing $p$-locally, we pass to a smaller algebra called an almost-source algebra, upon which a p-subgroup called the defect group acts as automorphisms. Three measures of the complexity of the block are, firstly, the defect group itself, secondly a finite category called the fusion system, thirdly a somewhat larger finite category called the Puig category. Each object of the Puig category comes with an associated multiplicity. We conjecture that those  multiplicities are invariant under the action of the fusion system. The conjecture has implications concerning the action of the defect group on a permuted basis of the almost-source algebra. By Clifford theory, the conjecture holds when the given group is p-solvable. This work is joint with Matthew Gelvin.

Date: Dec 9 2022

Saat: 14:30
 

Listing: https://researchseminars.org/seminar/7tepemathseminars