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The ring of polynomial functors of prime degree


Author: Alexander Zimmermann
Journal: Trans. Amer. Math. Soc. 367 (2015), 7161-7192
MSC (2010): Primary 16H10; Secondary 20C30, 20J06, 55R40
DOI: https://doi.org/10.1090/S0002-9947-2014-06265-X
Published electronically: December 17, 2014
MathSciNet review: 3378827
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Abstract: Let $ \hat {\mathbb{Z}}_p$ be the ring of $ p$-adic integers. We prove in the present paper that the category of polynomial functors from finitely generated free abelian groups to $ \hat {\mathbb{Z}}_p$-modules of degree at most $ p$ is equivalent to the category of modules over a particularly well understood ring, called Green order. This case was conjectured by Yuri Drozd.


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Additional Information

Alexander Zimmermann
Affiliation: Département de Mathématiques et CNRS UMR 7352, Université de Picardie, 33 rue St Leu, F-80039 Amiens Cedex 1, France
Email: alexander.zimmermann@u-picardie.fr

DOI: https://doi.org/10.1090/S0002-9947-2014-06265-X
Keywords: Polynomial functors, Green orders, Brauer tree algebras, Schur algebras, recollement diagram, representation type
Received by editor(s): April 17, 2013
Received by editor(s) in revised form: July 29, 2013, and August 12, 2013
Published electronically: December 17, 2014
Additional Notes: This research was supported by a grant “PAI alliance” from the Ministère des Affaires Étrangères de France and the British Council. The author acknowledges support from STIC Asie of the Ministère des Affaires Étrangères de France
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.