Congruence lattices of finite diagram monoids
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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.
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
Advances in Mathematics
© 2018 Elsevier Ltd. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.aim.2018.05.016
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