Stratifications and Mackey functors II: Globally defined Mackey functors

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Abstract

We describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero they form a highest weight category and we also determine precisely when this category is semisimple. This approach is used to show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite parts of it in some instances. We also develop a theory of vertices of globally defined Mackey functors in the spirit of group representation theory, as well as giving information about extensions between simple functors.

Original languageEnglish (US)
Pages (from-to)99-170
Number of pages72
JournalJournal of K-Theory
Volume6
Issue number1
DOIs
StatePublished - 2010

Bibliographical note

Funding Information:
Partially supported by the NSF and by MSRI

Keywords

  • Burnside ring
  • Mackey functor
  • biset
  • highest weight category
  • stratification

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