Brauer and Jones tied monoids

Francesca Aicardi; Diego Arcis; Jesús Juyumaya

doi:10.1016/j.jpaa.2022.107161

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arXiv · 2107.04170

Brauer and Jones tied monoids

Francesca Aicardi·Diego Arcis·Jesús Juyumaya

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Abstract

We introduce a ramified monoid, attached to each Brauer--type monoid, that is, to the symmetric group, to the Jones and Brauer monoids among others. Ramified monoids correspond to a class of tied monoids which arise from knot theory and are interesting in itself. The ramified monoid attached to the symmetric group is the Coxeter-like version of the so--called tied braid monoid. We give a presentation of the ramified monoid attached to the Brauer monoid. Also, we introduce and studied two tied-like monoids that cannot be described as ramified monoids. However, these monoids can also be regarded as tied versions of the Jones and Brauer monoids.

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BibTeX RIS

Francesca Aicardi, Diego Arcis, Jesús Juyumaya. 2021-07-09. Brauer and Jones tied monoids. https://doi.org/10.1016/j.jpaa.2022.107161

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