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- Title
The Hecke Algebra of a Frobenius P-Category.
- Authors
Puig, Lluis
- Abstract
We introduce a new avatar of a Frobenius P-category under the form of a suitable subring of the double Burnside ring of P - called the Hecke algebra of - where we are able to formulate: (i) the generalization to a Frobenius P-category of the Alperin Fusion Theorem, (ii) the 'canonical decomposition' of the morphisms in the exterior quotient of a Frobenius P-category restricted to the selfcentralizing objects as developed in chapter 6 of [4], and (iii) the 'basic P × P-sets' in chapter 21 of [4] with its generalization by Kari Ragnarsson and Radu Stancu to the virtual P × P-sets in [6]. We also explain the relationship with the usual Hecke algebra of a finite group.
- Subjects
HECKE algebras; FROBENIUS groups; FINITE groups; BURNSIDE rings; MATHEMATICAL decomposition; QUOTIENT rings; MORPHISMS (Mathematics)
- Publication
Algebra Colloquium, 2014, Vol 21, Issue 1, p1
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386714000029