Congruence lattices of finite diagram monoids

James East; James D. Mitchell; Nik Ruskuc; Michael Torpey

doi:10.1016/j.aim.2018.05.016

Congruence lattices of finite diagram monoids

James East, James D. Mitchell, Nik Ruskuc, Michael Torpey

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	931-1003
Number of pages	73
Journal	Advances in Mathematics
Volume	333
Early online date	15 Jun 2018
DOIs	https://doi.org/10.1016/j.aim.2018.05.016
Publication status	Published - 31 Jul 2018

Keywords

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

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10.1016/j.aim.2018.05.016

East_2018_AM_Congruencelattices_AAM
© 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
Accepted author manuscript, 760 KBLicence: CC BY-NC-ND

https://arxiv.org/abs/1709.00142

James David Mitchell
- jdm3st-andrews.acuk
Person: Academic
Nik Ruskuc
- nik.ruskucst-andrews.acuk
- School of Mathematics and Statistics - Director of Research
- Pure Mathematics - Professor
- Centre for Interdisciplinary Research in Computational Algebra
Person: Academic

Cite this

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title = "Congruence lattices of finite diagram monoids",

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AU - Mitchell, James D.

AU - Ruskuc, Nik

AU - Torpey, Michael

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AB - 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.

KW - Diagram monoids

KW - Partition monoids

KW - Brauer monoids

KW - Planar monoids

KW - Jones monoids

KW - Motzkin monoids

KW - Congruences

U2 - 10.1016/j.aim.2018.05.016

DO - 10.1016/j.aim.2018.05.016

M3 - Article

SN - 0001-8708

VL - 333

SP - 931

EP - 1003

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Congruence lattices of finite diagram monoids

Abstract

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James David Mitchell

Nik Ruskuc

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