Motzkin monoids and partial Brauer monoids

JOURNAL OF ALGEBRA

卷:471

Article

Dolinka, Igor¹  East, James²  Gray, Robert D.³ 

[1] Univ Novi Sad, Dept Math & Informat, Trg Dositeja Obradovica 4, Novi Sad 21101, Serbia

[2] Univ Western Sydney, Sch Comp Engn & Math, Ctr Res Math, Locked Bag 1797, Penrith, NSW 2751, Australia

[3] Univ East Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

关键词: Partial Brauer monoids;    Motzkin monoids;    Brauer monoids;    Idempotents;    Ideals;    Rank;    Idempotent rank;    Diagram algebras;    Partial Brauer algebras;    Motzkin algebras;    Cellular algebras;   

DOI  :  10.1016/j.jalgebra.2016.09.018

来源: Elsevier

【 摘 要 】

We study the partial Brauer monoid and its planar sub-monoid, the Motzkin monoid. We conduct a thorough investigation of the structure of both monoids, providing information on normal forms, Green's relations, regularity, ideals, idempotent generation, minimal (idempotent) generating sets, and so on. We obtain necessary and sufficient conditions under which the ideals of these monoids are idempotent-generated. We find formulae for the rank (smallest size of a generating set) of each ideal, and for the idempotent rank (smallest size of an idempotent generating set) of the idempotent-generated subsemigroup of each ideal; in particular, when an ideal is idempotent-generated, the rank and idempotent rank are equal. Along the way, we obtain a number of results of independent interest, and we demonstrate the utility of the semigroup theoretic approach by applying our results to obtain new proofs of some important representation theoretic results concerning the corresponding diagram algebras, the partial (or rook) Brauer algebra and Motzkin algebra. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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