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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2017
- DOI:
- 10.48550/arXiv.1709.00142
- arXiv:
- arXiv:1709.00142
- Bibcode:
- 2017arXiv170900142E
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Combinatorics;
- Mathematics - Rings and Algebras
- E-Print:
- V2: 49 pages, 13 figures, 4 tables - referee comments incorporated, to appear in Adv Math. V1: 47 pages, 12 figures, 3 tables