Related papers: The Bubble Algebra: Structure of a Two-Colour Temp…
We introduce multi-colour partition algebras $P_{n,m}(\delta_0, ..., \delta_{m-1})$, which are generalization of both bubble algebras and partition algebras, then define the bubble algebra $T_{n,m}(\delta_0, ..., \delta_{m-1})$ as a…
A method of constructing Temperley-Lieb algebras(TLA) representations has been introduced in [Xue \emph{et.al} arXiv:0903.3711]. Using this method, we can obtain another series of $n^{2}\times n^{2}$ matrices $U$ which satisfy the TLA with…
We investigate the representation theory of the valenced Temperley-Lieb algebras in mixed characteristic. These algebras, as described in characteristic zero by Flores and Peltola, arise naturally in statistical physics and conformal field…
We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the…
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…
The Kadar--Yu algebras are a physically motivated sequence of towers of algebras interpolating between the Brauer algebras and Temperley--Lieb algebras. The complex representation theory of the Brauer and Temperley--Lieb algebras is now…
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…
We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…
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…
Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated $L_\infty$ algebra giving rise to a fundamental…
The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of…
The definition of a dilute braid-monoid algebra is briefly reviewed. The construction of solvable vertex and interaction-round-a-face models built on representations of the dilute Temperley-Lieb and Birman-Wenzl-Murakami algebras is…
We define multi-colour generalizations of braid-monoid algebras and present explicit matrix representations which are related to two-dimensional exactly solvable lattice models of statistical mechanics. In particular, we show that the…
The Temperley-Lieb algebra \tln(\beta) can be defined as the set of rectangular diagrams with n points on each of their vertical sides, with all points joined pairwise by non-intersecting strings. The multiplication is then the…
In this paper, we present 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 (in the sense of Stembridge) of…
We give a new and conceptually straightforward proof of the well-known presentation for the Temperley-Lieb algebra, via an alternative new presentation. Our method involves twisted semigroup algebras, and we make use of two apparently new…
A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra. The $D^{(2)}_{n+1}$ vertex models are examples of corresponding solvable lattice models…
We introduce stability categories for diagram algebras---analogues to Randal-Williams and Wahl's homogeneous categories. We use these to study representation stability properties of the Temperley--Lieb algebras, the Brauer algebras, and the…
A generalization of the Yang-Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang-Baxter equation still ensures that the transfer matrix generates operators in…
Working in the dense loop representation, we use the planar Temperley-Lieb algebra to build integrable lattice models called logarithmic minimal models LM(p,p'). Specifically, we construct Yang-Baxter integrable Temperley-Lieb models on the…