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Idempotents in the Endomorphism Algebra of a Finite Lattice

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Abstract

We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T. This idempotent is associated with all possible sublattices of T which are totally ordered. A generalization is considered in a conjectural fashion and proved experimentally to hold in many cases.

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Authors and Affiliations

  1. CNRS-LAMFA, Université de Picardie - Jules Verne, 33, rue St Leu, F-80039, Amiens Cedex 1, France

    Serge Bouc

  2. Institut de mathématiques, EPFL, Station 8, CH-1015, Lausanne, Switzerland

    Jacques Thévenaz

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  1. Serge Bouc
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  2. Jacques Thévenaz
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Correspondence to Jacques Thévenaz.

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Bouc, S., Thévenaz, J. Idempotents in the Endomorphism Algebra of a Finite Lattice. Order 39, 485–504 (2022). https://doi.org/10.1007/s11083-021-09588-x

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  • DOI: https://doi.org/10.1007/s11083-021-09588-x

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