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2012 On unstable modules over the Dickson algebras, the Singer functors $R_s$ and the functors $\mathrm{Fix}_s$
Geoffrey M L Powell
Algebr. Geom. Topol. 12(4): 2451-2491 (2012). DOI: 10.2140/agt.2012.12.2451

Abstract

The category DsU 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 DsU. 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 DsU. In addition, the right adjoint s to Rs is introduced and is related to the indecomposables functor and the functor Fixs.

Citation

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Geoffrey M L Powell. "On unstable modules over the Dickson algebras, the Singer functors $R_s$ and the functors $\mathrm{Fix}_s$." Algebr. Geom. Topol. 12 (4) 2451 - 2491, 2012. https://doi.org/10.2140/agt.2012.12.2451

Information

Received: 6 December 2010; Revised: 5 July 2012; Accepted: 2 August 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1263.55004
MathSciNet: MR3020213
Digital Object Identifier: 10.2140/agt.2012.12.2451

Subjects:
Primary: 55S10
Secondary: 18E10

Rights: Copyright © 2012 Mathematical Sciences Publishers

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