2011/01/06 by Lluis Puig, Puig, Lluis
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1101.1288
arxiv created 2011/01/06 · arxiv updated 2011/01/07
We introduce a new avatar of a Frobenius P-category F in the form of a suitable sub-ring HF of the double Burnside ring of P - called the Hecke algebra of F - where we are able to formulate the generalization to a Frobenius P-category of the Alperin Fusion Theorem, the "canonical decomposition" of the morphisms in the exterior quotient of a Frobenius P-category restricted to the selfcentralizing objects as developed in the chapter 6 of [4], the "basic P X P-sets" in the chapter 21 of [4], and the generalization by Kari Ragnarsson and Radu Stancu to the virtual P X P-sets in [6]. We also explain the relationship with the usual Hecke algebra a of finite group.