Brauer-friendly modules and slash functors
- Autores: Erwan Biland
- Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 218, Nº 12, 2014, págs. 2319-2336
- Idioma: inglés
- DOI: 10.1016/j.jpaa.2014.04.003
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Resumen
This paper introduces the notion of Brauer-friendly modules , a generalisation of endo-p -permutation modules. A module over a block algebra OGeOGe is said to be Brauer-friendly if it is a direct sum of indecomposable modules with compatible fusion-stable endopermutation sources. We obtain, for these modules, a functorial version of Dade's slash construction, also known as deflation�restriction. We prove that our slash functors , defined over Brauer-friendly categories , share most of the very useful properties that are satisfied by the Brauer functor over the category of p -permutation OGe-modulesOGe-modules. In particular, we give a parametrisation of indecomposable Brauer-friendly modules, which opens the way to a complete classification whenever the fusion-stable sources are classified. Those tools have been used by the author in [4] to prove the existence of a stable equivalence between non-principal blocks in the context of a minimal counterexample to the odd Zp?-theorem.
