Related papers: Virtual Extension of Temperley--Lieb Algebra
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…
Virtual knot theory has experienced a lot of nice features that did not appear in classical knot theory, e.g., parity and picture-valued invariants. In the present paper we use virtual knot theory effects to construct new representations of…
We show that two well-studied classes of tame algebras coincide: namely, the class of symmetric special biserial algebras coincides with the class of Brauer graph algebras. We then explore the connection between gentle algebras and…
In this survey we collect all results regarding the construction of the Framization of the Temperley-Lieb algebra of type $A$ as a quotient algebra of the Yokonuma-Hecke algebra of type $A$. More precisely, we present all three possible…
Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics: Knot Theory, Categorical Quantum Mechanics, and Logic and Computation. We…
We determine the image of the braid groups inside the Temperley-Lieb algebras, defined over finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter. We also prove that, under…
The Temperley-Lieb algebra may be thought of as a quotient of the Hecke algebra of type A, acting on tensor space as the commutant of the usual action of quantum sl(2) on the n-th tensor power of the 2-dimensional irreducible module. We…
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 2015 Hikami and Inoue constructed a representation of the braid group in terms of cluster algebra associated with the decomposition of the complement of the corresponding knot into ideal hyperbolic tetrahedra. This representation leads…
We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.
Important developments in fault-tolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco…
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.
The Temperley-Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley-Lieb algebra. Our results apply to the framework which…
Finite Temperley-Lieb (TL) algebras are diagram-algebra quotients of (the group algebra of) the famous Artin's braid group $B_N$, while the affine TL algebras arise as diagram algebras from a generalized version of the braid group. We study…
Twisted knot theory introduced by M. Bourgoin is a generalization of knot theory. It leads us to the notion of twisted virtual braids. In this paper we show theorems for twisted links corresponding to the Alexander theorem and the Markov…
We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebra, its partial analogue, walled Brauer algebra, its partial analogue, Temperley-Lieb algebra, its…
This article examines the growth of generalized algebras of type Temperley-Lieb $ TL _ {\ Gamma, \ tau}. $ Studied them dimension or if the algebra of infinite growth.
In this paper, we describe the irreducible representations and give a dimension formula for the Framisation of the Temperley-Lieb algebra. We then prove that the Framisation of the Temperley-Lieb algebra is isomorphic to a direct sum of…
Based on the Temperley--Lieb algebra we define a class of one-dimensional Hamiltonians with nearest and next-nearest neighbour interactions. Using the regular representation we give ground states of this model as words of the algebra. Two…
We investigate the representation theory of the Temperley-Lieb algebra, $TL_n(\delta)$, defined over a field of positive characteristic. The principle question we seek to answer is the multiplicity of simple modules in cell modules for…