• DOI:10.1142/S1005386714000029
• Corpus ID: 119610663

The Hecke algebra of a Frobenius P-category

@article{Puig2011TheHA,
  title={The Hecke algebra of a Frobenius P-category},
  author={Lluis Puig},
  journal={arXiv: Group Theory},
  year={2011}
}

• L. Puig
• Published 6 January 2011
• Mathematics
• arXiv: Group Theory

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.