Idempotents in the Endomorphism Algebra of a Finite Lattice

Serge Bouc (1) , Jacques Thévenaz (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 Section de Mathematiques [Lausanne]

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.

Domaines: Mathématiques [math]

Serge Bouc, Jacques Thévenaz. Idempotents in the Endomorphism Algebra of a Finite Lattice. Order, 2022, 39 (3), pp.485-504. ⟨10.1007/s11083-021-09588-x⟩. ⟨hal-04009372⟩