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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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- Serge Bouc and Jacques Thévenaz, Correspondence functors and finiteness conditions, J. Algebra 495 (2018), 150–198. MR 3726107, DOI https://doi.org/10.1016/j.jalgebra.2017.11.010
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- Richard P. Stanley, Enumerative combinatorics. Volume 1, 2nd ed., Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 2012. MR 2868112
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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