Idempotents in the Endomorphism Algebra of a Finite Lattice

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...

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Bibliographic Details
Published in:Order (Dordrecht) 2022-10, Vol.39 (3), p.485-504
Main Authors: Bouc, Serge, Thévenaz, Jacques
Format: Article
Language:English
Subjects:
Algebra
Discrete Mathematics
Lattices
Lattices (mathematics)
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Subgroups
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Summary: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.
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-021-09588-x