The algebra of Boolean matrices, correspondence functors, and simplicity

DOI10.4171/JCA/44zbMath1484.06022arXiv1902.05422MaRDI QIDQ2210589

Serge Bouc, Jacques Thévenaz

Publication date: 7 November 2020

Published in: Journal of Combinatorial Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.05422

zbMATH Keywords

latticeposetsimple modulerelationcorrespondenceBoolean matrixfunctor categoryfinite setsimple functor

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Representations of orders, lattices, algebras over commutative rings (16G30) Module categories in associative algebras (16D90) Representation theory of lattices (06B15) Structure theory of Boolean algebras (06E05) Preorders, orders, domains and lattices (viewed as categories) (18B35) Representation of semigroups; actions of semigroups on sets (20M30) Functor categories, comma categories (18A25) Categories of sets, characterizations (18B05) Categories of spans/cospans, relations, or partial maps (18B10)

Related Items (6)

Ehresmann theory and partition monoids ⋮ Representations of finite sets and correspondences ⋮ Simple and projective correspondence functors ⋮ Idempotents in the endomorphism algebra of a finite lattice ⋮ Correspondence functors and duality ⋮ Germs in a poset

Uses Software

• GAP

Cites Work

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• Correspondence functors and finiteness conditions
• Algebras of Ehresmann semigroups and categories
• Set functors equipped with a double action
• Structure of the rational monoid algebra for Boolean matrices of order 3
• Möbius functions and semigroup representation theory.
• Cardinalities of \(D\)-classes in B\(_n\)
• On the Semigroup Algebra of Binary Relations
• On the irreducible representations of a finite semigroup
• Linear Representations of Semigroups of Boolean Matrices
• On the semigroup of binary relations on a finite set
• On the semigroup of binary relations

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