Mackey Functors with Chain Conditions

Luca, Florian

doi:10.1006/jabr.1997.7417

Cited by 1 publication

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References 7 publications

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“…The ∇ H,U were first defined in different notation by Lewis [8] and several of the statements we make in this section were familiar to him. They also play an important role in the work of Luca [9], who describes a number of their properties. When H and K are subgroups of G we will write…”

Section: The ∆ and ∇ Functorsmentioning

confidence: 99%

Stratifications and Mackey Functors I: Functors For a Single Group

Webb

2001

Proceedings of the London Mathematical Society

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In the context of Mackey functors we introduce a category which is analogous to the category of modules for a quasi-hereditary algebra which have a filtration by standard objects. Many of the constructions which work for quasi-hereditary algebras can be done in this new context. In particular we construct an analogue of the 'Ringel dual', which turns out here to be a standardly stratified algebra. The Mackey functors which play the role of the standard objects are constructed in the same way as functors which have been previously used in parametrizing the simple Mackey functors, but instead of using simple modules in their construction (as was done before) we use p-permutation modules. These Mackey functors are obtained as adjoints of the operations of forming the Brauer quotient and its dual. The filtrations which have these Mackey functors as their factors are closely related to the filtrations whose terms are the sum of induction maps from specified subgroups, or are the common kernel of restriction maps to these subgroups.

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Section: The ∆ and ∇ Functorsmentioning

confidence: 99%

Stratifications and Mackey Functors I: Functors For a Single Group

Webb

2001

Proceedings of the London Mathematical Society

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Mackey Functors with Chain Conditions

Cited by 1 publication

References 7 publications

Stratifications and Mackey Functors I: Functors For a Single Group

Stratifications and Mackey Functors I: Functors For a Single Group

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