A braids and ties algebra of type B

Flores, Marcelo

doi:10.1016/j.jpaa.2019.04.011

Cited by 7 publications

(9 citation statements)

References 17 publications

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“…Firstly, observe that, by applying Theorems 4 and 5, we have a correspondence between isotopy classes of T ST and the set of equivalence classes in T B B ∞ (according to ∼ M ). Secondly, we define a natural representation from T B B n into the algebra an algebra of braids and ties of type B [6]. This algebra supports a Markov trace, hence we may apply Jones' method to obtain the invariant ∆ B .…”

Section: The Invariant F B Via Jones' Methodsmentioning

confidence: 99%

“…In this section, we introduce the tied braid monoid of type B in order to obtain analogues for Alexander and Markov theorems for tied links in ST . This, with the aim of recovering F B via Jones' method using the algebra of braids and ties of type B and the respective Markov trace defined in [6] .…”

Section: The Tied Braid Monoid Of Type Bmentioning

confidence: 99%

“…This algebra supports a Markov trace (see [7,Theorem 3]), consequently invariants for framed knots and links in the solid torus are obtained by applying Jones' method. In order to generalize the classical bt-algebra, in [6], a braids and ties algebra of type B is introduced, denoted by…”

Section: Introductionmentioning

confidence: 99%

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Tied links in the solid torus

Flores¹

2019

Preprint

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Section: The Invariant F B Via Jones' Methodsmentioning

confidence: 99%

Section: The Tied Braid Monoid Of Type Bmentioning

confidence: 99%

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Tied links in the solid torus

Flores¹

2019

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“…In this section we give a mechanism to construct algebras from tied monoids, we call these algebras tied algebras. This mechanism produce the Hecke algebras, bt-algebras of type A [5], as well to those bt-algebras of type B defined in [21,14]. At the end of the paper we show out the tied algebra obtained from the monoid Let T Γ M be the tied monoid of M respect to P associated to φ.…”

Section: Tied Algebrasmentioning

confidence: 96%

“…(20)]. The mechanism captures the classical Hecke algebras, the bt-algebra defined in [1], as well the bt-algebras defined by Flores [14] and Marin [21].…”

Section: Introductionmentioning

confidence: 99%

Tied Monoids

Arcis¹,

Juyumaya²

2020

Preprint

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We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids indicate that they should give origin to new knot algebras; indeed, our tied monoids include the tied braid monoid and the tied singular braid monoid, which were used, respectively, to construct new polynomial invariants for classical links and singular links. Consequently, we provide a mechanism to attach an algebra to each tied monoid. To build the tied monoids it is necessary to find presentations of set partition monoids of types A, B and D, among others; these presentations are interesting in their own right and seem to be absent in the literature.

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Tied monoids

Arcis

Juyumaya

2021

Semigroup Forum

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We introduce two new algebras that we call tied-boxed Hecke algebra and tied-boxed Temperley-Lieb algebra. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second one is a tied-version of the well known Temperley-Lieb algebra. We study their representation theory and give cellular bases for them. Furthermore, we explore a strong connection between the tied-boxed Temperley-Lieb algebra and the so-called partition Temperley-Lieb algebra given by Juyumaya. Also, we show that both structures inherit diagrammatic interpretations from a new class of monoids that we call boxed ramified monoids. Additionally, we give presentations for the singular part of the ramified symmetric monoid and for the boxed ramified monoid associated to the Brauer monoid.

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A braids and ties algebra of type B

Cited by 7 publications

References 17 publications

Tied links in the solid torus

Tied links in the solid torus

Tied Monoids

Tied monoids

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