The Hecke algebra of a Frobenius P-category
Group Theory
2011-01-07 v1
Abstract
We introduce a new avatar of a Frobenius P-category F in the form of a suitable sub-ring H_F 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.
Keywords
Cite
@article{arxiv.1101.1288,
title = {The Hecke algebra of a Frobenius P-category},
author = {Lluis Puig},
journal= {arXiv preprint arXiv:1101.1288},
year = {2011}
}