Congruence lattices of finite diagram monoids
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 I → M onto the minimal ideal, a congruence on M, and a normal subgroup of a maximal subgroup outside I.
Citation
East , J , Mitchell , J D , Ruskuc , N & Torpey , M 2018 , ' Congruence lattices of finite diagram monoids ' , Advances in Mathematics , vol. 333 , pp. 931-1003 . https://doi.org/10.1016/j.aim.2018.05.016
Publication
Advances in Mathematics
Status
Peer reviewed
ISSN
0001-8708Type
Journal article
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