相关论文: Dual presentation and linear basis of the Temperle…

Graham and Lehrer (1998) introduced a Temperley-Lieb category $\mathsf{\widetilde{TL}}$ whose objects are the non-negative integers and the morphisms in $\mathsf{Hom}(n,m)$ are the link diagrams from $n$ to $m$ nodes. The Temperley-Lieb…

We study representations of the loop braid group $LB_n$ from the perspective of extending representations of the braid group $B_n$. We also pursue a generalization of the braid/Hecke/Temperlely-Lieb paradigm---uniform finite dimensional…

The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called…

Let G be the fundamental group of the complement of a K(G,1) hyperplane arrangement (such as Artin's pure braid group) or more generally a homologically toroidal group (as defined in the paper). The subgroup of elements in the complex…

We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras of type D. We prove that the cyclotomic Temperley-Lieb algebras of type D are…

We construct a faithful categorical action of the type $B$ braid group on the bounded homotopy category of finitely generated projective modules over a finite dimensional algebra which we call the type $B$ zigzag algebra. This categorical…

In this paper, we explore algebraic structures and low dimensional topology underlying quantum information and computation. We revisit quantum teleportation from the perspective of the braid group, the symmetric group and the virtual braid…

We study some algebraic and combinatorial features of two algebras that arise as quotients of Temperley-Lieb algebras of type $\tilde{C}$, namely, the two-boundary Temperley-Lieb algebra and the symplectic blob algebra. We provide a…

Inspired by earlier works on representations of the Temperley-Lieb algebra we introduce a novel family of representations of the algebra. This may be seen as a generalization of the so called asymmetric twin representation. The underlying…

This article concerns a generalization of the Temperley-Lieb algebra, important in applications to conformal field theory. We call this algebra the valenced Temperley-Lieb algebra. We prove salient facts concerning this algebra and its…

In a previous paper, we presented an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley--Lieb algebra having a basis indexed by the fully commutative elements of the Coxeter group of…

We derive a Laurent series expansion for the structure coefficients appearing in the dual basis corresponding to the Kauffman diagram basis of the Temperley-Lieb algebra $\text{TL}_k(d)$, converging for all complex loop parameters $d$ with…

The Hamiltonian of the $N$-state clock model is written in terms of a coupled Temperley-Lieb (TL) algebra defined by $N-1$ types of TL generators. This generalizes a previous result for $N=3$ obtained by J. F. Fjelstad and T. M\r{a}nsson…

We show that the Temperley-Lieb algebra of type $A$ and the blob algebra (also known as the Temperley-Lieb algebra of type $ B$) at roots of unity are $ \mathbb Z$-graded algebras.We moreover show that they are graded cellular algebras,…

We explicitly describe the category of modules of the Temperley-Lieb algebra $\mathrm{TL}_n(\beta)$ under specialization $\beta=0$ for even $n$ in terms of a quiver algebra, analogous to a result of Berest-Etingof-Ginzburg. In particular,…

In this paper, we will study the Dieck-Temlerley-Lieb algebras of type Bn and Cn. We compute their ranks and describe a basis for them by using some results from corresponding Brauer algebras and Temperley-Lieb algebras.

In a previous work [11], the author considered a representation of the braid group \rho: B_n\to GL_m(\Bbb Z[q^{\pm 1},t^{\pm 1}]) (m=n(n-1)/2), and proved it to be faithful for n=4. Bigelow [3] then proved the same representation to be…

To a plane algebraic curve of degree n, Moishezon associated a braid monodromy homomorphism from a finitely generated free group to Artin's braid group B_n. Using Hansen's polynomial covering space theory, we give a new interpretation of…

Construction of the diagrammatic version of the affine Temperley-Lieb algebra of type $\widetilde{A_N}$ as a subring of matrices over the Laurent polynomials is given. We move towards geometrical understanding of cellular structure of the…

New sets of rank n-representations of Temperley-Lieb algebra TL_N(q) are constructed. They are characterized by two matrices obeying a generalization of the complex Hadamard property. Partial classifications for the two matrices are given,…