Congruence lattices of finite diagram monoids

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Abstract

We give a complete description of the congruence lattices of the following finite diagram monoids: the partition monoid, the planar partition monoid, the Brauer monoid, the Jones monoid (also known as the Temperley–Lieb monoid), the Motzkin monoid, and the partial Brauer monoid. All the congruences under discussion arise as special instances of a new construction, involving an ideal I , a retraction IM onto the minimal ideal, a congruence on M, and a normal subgroup of a maximal subgroup outside I.
Original languageEnglish
Pages (from-to)931-1003
Number of pages73
JournalAdvances in Mathematics
Volume333
Early online date15 Jun 2018
DOIs
Publication statusPublished - 31 Jul 2018

Keywords

  • Diagram monoids
  • Partition monoids
  • Brauer monoids
  • Planar monoids
  • Jones monoids
  • Motzkin monoids
  • Congruences

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