https://hal.archives-ouvertes.fr/hal-01389189Powell, GeoffreyGeoffreyPowellLAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche ScientifiqueOn unstable modules over the Dickson algebras, the Singer functors Rs and the functors FixsHAL CCSD2012[MATH] Mathematics [math]Univ Angers, Okina2016-10-28 10:22:542021-11-16 09:52:052016-10-28 10:22:54enJournal articles10.2140/agt.2012.12.24511<p>The category Ds–U of unstable modules over the Steenrod algebra equipped with a compatible module structure over the Dickson algebra Ds is studied at the prime 2, with applications to the Singer functor Rs, considered as a functor from unstable modules U to Ds–U. An explicit copresentation of RsM is given using Lannes’ T–functor when M is a reduced unstable module; applying Lannes’ functor Fixs, this is used to show that Rs gives a fully-faithful embedding of U in Ds–U. In addition, the right adjoint ℨs to Rs is introduced and is related to the indecomposables functor and the functor Fixs.</p>