A complete classification of endomorphisms of Kiselman's semigroup

2025/06/04 by Andrensek, Luka
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2506.03604

Abstract

Kiselman's semigroup K_n was studied by Kudryavtseva and Mazorchuk, who posed the question of whether it is possible to classify all endomorphisms of K_n. In this paper, we provide a complete classification of endomorphisms of K_n and present a Boolean matrix monoid that is isomorphic to End(K_n).

Citations

• The cardinality of Kiselman's semigroups grows double-exponentially
• Irreducible representations of Hecke-Kiselman monoids
• The word problem for Hecke--Kiselman monoids of type A_n and \widetildeA_n
• Gröbner basis and the automaton property of Hecke--Kiselman algebras
• The Finite Basis Problem for Kiselman Monoids
• A graph-dynamical interpretation of Kiselman's semigroups

Related

• Endomorphisms of semigroups of oriented transformations
• The structure of End(T_n)
• Endomorphisms of semigroups of monotone transformations
• On monoids of endomorphisms of a cycle graph
• On the endomorphism monoid of a profinite semigroup