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 language | English (US) |
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Pages (from-to) | 99-170 |
Number of pages | 72 |
Journal | Journal of K-Theory |
Volume | 6 |
Issue number | 1 |
DOIs | |
State | Published - 2010 |
Bibliographical note
Funding Information:Partially supported by the NSF and by MSRI
Keywords
- Burnside ring
- Mackey functor
- biset
- highest weight category
- stratification