Middle East Technical University General Seminars

Blocks and characteristic bisets of fusion systems
Matthew Gelvin
Bilkent University, Turkey
Özet : Let G be a finite group, p a prime dividing the order of G, and k an algebraically closed field of characteristic p. If B is a block algebra of kG and S a Sylow p-subgroup of G, B possesses a k-basis X that is invariant under the left and right multiplicative actions of S. X can be viewed as an (S,S)-biset, and as such is determined up to isomorphism by the (kS,kS)-bimodule structure of B; conversely, X determines B as a (kS,kS)-bimodule. In this talk we will relate the biset structure of X to the p-fusion of G: Explicitly, X is a semicharacteristic biset for the fusion system on S induced by G. This observation imposes certain constraints on the module structure of B. We will give a brief introduction to the notion of fusion system, describe the role of semicharacteristic bisets in the theory, and explain how the relation can be used to see that certain group algebras have no nontrivial block decompositions. The last point represents joint work with Justin Lynd, in which we conjecture a new characterization of characteristic-p groups.
  Tarih : 07.03.2019
  Saat : 15:40
  Yer : Gündüz İkeda Seminar Rooom
  Dil : English