Stratifications and Mackey Functors II: Globally Defined Mackey Functors
نویسندگان
چکیده
منابع مشابه
Stratifications and Mackey Functors Ii: Globally Defined Mackey Functors
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 pa...
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Let G be a finite group. In [5], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for G and biset functors defined on subgroups of G and bifree bisets as morphisms. This paper proposes a different approach to this problem, from the point of view of various categories of G-sets. In particular, the category G-set of fused G-sets is introduced, as well as th...
متن کاملMackey Functors and Bisets
For any finite group G, we define a bifunctor from the Dress category of finite G-sets to the conjugation biset category, whose objects are subgroups of G, and whose morphisms are generated by certain bifree bisets. Any additive functor from the conjugation biset category to abelian groups yields a Mackey functor by composition. We characterize the Mackey functors which arise in this way.
متن کاملResolutions of Mackey functors
I will build some standard resolutions for Mackey functors which are projective relative to p-subgroups. Those resolutions are closely related to the poset of p-subgroups. They lead to generalizations of known results on cohomology. They give a way to compute the Cartan matrix for Mackey functors, in terms of p-permutation modules, and to precise the structure of projective Mackey functors. The...
متن کاملThe Structure of Mackey Functors
Mackey functors are a framework having the common properties of many natural constructions for finite groups, such as group cohomology, representation rings, the Bumside ring, the topological K-theory of classifying spaces, the algebraic K-theory of group rings, the Witt rings of Galois extensions, etc. In this work we first show that the Mackey functors for a group may be identified with the m...
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ژورنال
عنوان ژورنال: Journal of K-Theory
سال: 2010
ISSN: 1865-2433,1865-5394
DOI: 10.1017/is009010011jkt095