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Representation Theory

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Simple and projective correspondence functors


Authors: Serge Bouc and Jacques Thévenaz
Journal: Represent. Theory 25 (2021), 224-264
MSC (2020): Primary 06B05, 06B15, 06D05, 06D50, 16B50, 18B05, 18B10, 18B35, 18E05
DOI: https://doi.org/10.1090/ert/564
Published electronically: April 2, 2021
MathSciNet review: 4238629
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Abstract: A correspondence functor is a functor from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple modules are projective for the algebra of all relations on a finite set. Moreover, we analyze the occurrence of such simple projective functors inside the correspondence functor $F$ associated with a finite lattice and we deduce a direct sum decomposition of $F$.


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Additional Information

Serge Bouc
Affiliation: CNRS-LAMFA, Université de Picardie - Jules Verne, 33, rue St Leu, F-80039 Amiens Cedex 1, France
MR Author ID: 207609
ORCID: 0000-0003-2330-1845
Email: serge.bouc@u-picardie.fr

Jacques Thévenaz
Affiliation: Institut de mathématiques, EPFL, Station 8, CH-1015 Lausanne, Switzerland
ORCID: 0000-0001-8820-3627
Email: jacques.thevenaz@epfl.ch

Keywords: Finite set, correspondence, functor category, simple functor, poset, lattice.
Received by editor(s): September 7, 2020
Received by editor(s) in revised form: January 12, 2021
Published electronically: April 2, 2021
Article copyright: © Copyright 2021 American Mathematical Society