Geodesic
On unstable modules over the Dickson algebras, the Singer functors Rs and the functors Fixs
Powell, Geoffrey M L1
1Laboratoire Angevin de Recherche en Mathématiques, UMR 6093, Faculté des Sciences, Université d’Angers, 2 Boulevard Lavoisier, 49045 Angers, France
Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 2451-2491
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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.

DOI : 10.2140/agt.2012.12.2451
Classification : 55S10, 18E10
Keywords: Dickson algebra, Singer functor, unstable module, Lannes' $T$–functor, Fix

Powell, Geoffrey M L  1

1 Laboratoire Angevin de Recherche en Mathématiques, UMR 6093, Faculté des Sciences, Université d’Angers, 2 Boulevard Lavoisier, 49045 Angers, France 
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Powell, Geoffrey M L. On unstable modules over the Dickson algebras, the Singer functors Rs and the functors Fixs. Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 2451-2491. doi: 10.2140/agt.2012.12.2451

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