The Hecke Algebra of a Frobenius P-Category

• 作者: Lluis Puig
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 代数 Frobenius 标准分解 iii 有限群 集合 子环 定理
• 年，卷（期）: 2014,（1）
• 页码范围: 1-52
• 页数: 52页
• 分类号: O152.6
• 语种: 中文

摘要

We introduce a new avatar of a Frobenius P-category F under the form of a suitable subring HF of the double Burnside ring of P -- called the Hecke algebra of F- 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.