Representation theory of monoids consisting of order-preserving functions and order-reversing functions on an n -set
Abstract
We consider the monoid of order-preserving functions and order-reversing functions on an n-set. Over a field of characteristic not 2, we obtain a quiver presentation for the monoid algebra: two straight paths with n−1 and n vertices, respectively, and all compositions are zero. We also classify homomorphisms between induced left Schützenberger modules. We define a covering monoid with a distinction between order-preserving and order-reversing constant functions. We show that the algebra of the covering monoid is isomorphic to the direct product of two copies of the algebra of the monoid of all order-preserving functions on an n-set.
Fields of Study & Subjects
Advanced Algebra and Logic
semigroups and automata theory
Rings
Modules
and Algebras
Publication details
- Journal / source
- Communications in Algebra
- Volume
- 54
- Issue
- 6
- Pages
- 2726–2749
- Publication date
- 4 January 2026
- Language
- EN