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arXiv · 2208.07125

Green correspondence on centric Mackey functor over fusion systems

Marco Praderio Bova
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Abstract

In this paper we give a definition of (centric) Mackey functor over a fusion system which generalizes the notion of Mackey functor over a group. In this context we prove that, given some conditions on a related ring, the centric Burnside ring over a fusion system (as defined by Diaz and Libman) acts on any centric Mackey functor. We also prove that the Green correspondence holds for centric Mackey functors over fusion systems. As a means to prove this we introduce a notion of relative projectivity for centric Mackey functors over fusion systems and provide a decomposition of a particular product in $\mathcal{O}\left(\mathcal{F}^c\right)_{\sqcup}$ in terms of the product in $\mathcal{O}\left(N_{\mathcal{F}}\left(H\right)^c\right)_{\sqcup}$.

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BibTeXRIS

Marco Praderio Bova. 2022-08-15. Green correspondence on centric Mackey functor over fusion systems. https://doi.org/10.1016/j.jalgebra.2023.09.041

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