The dominant dimension of cohomological Mackey functors
نویسندگان
چکیده
منابع مشابه
Complexity and cohomology of cohomological Mackey functors
Let k be a field of characteristic p > 0. Call a finite group G a poco group over k if any finitely generated cohomological Mackey functor for G over k has polynomial growth. The main result of this paper is that G is a poco group over k if and only if the Sylow p-subgroups of G are cyclic, when p > 2, or have sectional rank at most 2, when p = 2. A major step in the proof is the case where G i...
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This is a report on some recent joint work with Radu Stancu, to appear in [4]. It is an expanded version of a talk given at the RIMS workshop Cohomology of finite groups and related topics, February 18-20, 2015. 1. Cohomological Mackey functors 1.1. Let G be a finite group, and k be a commutative ring. There are many equivalent definitions of Mackey functors for G over k. For the “naive” one, t...
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Let k be a field of characteristic p. We construct a new inflation functor for cohomological Mackey functors for finite groups over k. Using this inflation functor, we give an explicit presentation of the graded algebra of self extensions of the simple functor S 1 , when p is odd and G is an elementary abelian p-group. AMS Subject Classification : 18A25, 18G10, 18G15, 20J05.
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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 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...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2018
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498818502286