Virtual an arrow Temperley--Lieb algebras, Markov traces, and virtual link invariants - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Virtual an arrow Temperley--Lieb algebras, Markov traces, and virtual link invariants

Luis Paris
  • Fonction : Auteur
  • PersonId : 900472
Loïc Rabenda
  • Fonction : Auteur
  • PersonId : 1077289

Résumé

Let R f = Z[A ±1 ] be the algebra of Laurent polynomials in the variable A and let R a = Z[A ±1 , z 1 , z 2 ,. .. ] be the algebra of Laurent polynomials in the variable A and standard polynomials in the variables z 1 , z 2 ,. .. . For n ≥ 1 we denote by VB n the virtual braid group on n strands. We define two towers of algebras {VTL n (R f)} ∞ n=1 and {ATL n (R a)} ∞ n=1 in terms of diagrams. For each n ≥ 1 we determine presentations for both, VTL n (R f) and ATL n (R a). We determine sequences of homomorphisms {ρ f n : R f [VB n ] → VTL n (R f)} ∞ n=1 and {ρ a n : R a [VB n ] → ATL n (R a)} ∞ n=1 , we determine Markov traces {T f n : VTL n (R f) → R f } ∞ n=1 and {T a n : ATL n (R a) → R a } ∞ n=1 , and we show that the invariants for virtual links obtained from these Markov traces are the f-polynomial for the first trace and the arrow polynomial for the second trace. We show that, for each n ≥ 1, the standard Temperley-Lieb algebra TL n embeds into both, VTL n (R f) and ATL n (R a), and that the restrictions to {TL n } ∞ n=1 of the two Markov traces coincide.
Fichier principal
Vignette du fichier
210531ParRabV3.pdf (407.08 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02940188 , version 1 (16-09-2020)
hal-02940188 , version 2 (10-06-2021)

Identifiants

Citer

Luis Paris, Loïc Rabenda. Virtual an arrow Temperley--Lieb algebras, Markov traces, and virtual link invariants. 2021. ⟨hal-02940188v2⟩
88 Consultations
114 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More