A filtration of the modular representation functor
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- 作者：Ergü ; n Yaraneri
- 关键词：Modular representation algebra ; Biset functor ; Inflation functor ; (Global) Mackey functor ; Composition factors ; Multiplicity ; Filtration
- 刊名：Journal of Algebra
- 出版年：2007
- 出版时间：1 December 2007
- 年：2007
- 卷：318
- 期：1
- 页码：140-179
- 全文大小：352 K
文摘
Let ![]()
and ![]()
be algebraically closed fields of characteristics p>0 and 0, respectively. For any finite group G we denote by ![]()
the modular representation algebra of G over ![]()
where ![]()
is the Grothendieck group of finitely generated ![]()
-modules with respect to exact sequences. The usual operations induction, inflation, restriction, and transport of structure with a group isomorphism between the finitely generated modules of group algebras over ![]()
induce maps between modular representation algebras making ![]()
an inflation functor. We show that the composition factors of ![]()
are precisely the simple inflation functors ![]()
where C ranges over all nonisomorphic cyclic p′-groups and V ranges over all nonisomorphic simple ![]()
-modules. Moreover each composition factor has multiplicity 1. We also give a filtration of ![]()
.