Browsing by Author "Webb, Peter"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Resolutions, relation modules and Schur multipliers for categories
    (2008-09-15) Webb, Peter
    We show that the construction in group cohomology of the Gruenberg resolution associated to a free presentation and the resulting relation module can be copied in the context of representations of categories. We establish five-term exact sequences in the cohomology of categories and go on to show that the Schur multiplier of the category has properties which generalize those of the Schur multiplier of a group.
  • Thumbnail Image
    Item
    Stratifications and Mackey functors II: globally defined Mackey functors
    (2008-09-16) Webb, Peter
    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.