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Stratifications and Mackey functors II: globally defined Mackey functors

Webb, Peter
2008-09-16
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Stratifications and Mackey functors II: globally defined Mackey functors

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2008-09-16

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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.

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Webb, Peter. (2008). Stratifications and Mackey functors II: globally defined Mackey functors. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/43181.

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