Related papers: Presentations for the ghost algebra and the label …
The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $\TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector…
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…
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…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
The Antimagic Graph Conjecture asserts that every connected graph $G = (V, E)$ except $K_2$ admits an edge labeling such that each label $1, 2, \dots, |E|$ is used exactly once and the sums of the labels on all edges incident to a given…
Let (W,S) be a Coxeter system of affine type D, and let TL(W) the corresponding generalized Temperley-Lieb algebra. In this extended abstract we define an infinite dimensional associative algebra made of decorated diagrams which is…
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…
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…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
In a labeling scheme the vertices of a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. A representation of a graph from that class is given by the set of…
A host algebra generalises the concept of a group algebra as follows. Let F be a unital C*-algebra, and let S_0 be a proper subset of its states within which one wants to keep the analysis (e.g. F is the group algebra of a discrete group G,…
A null vector is an algebraic quantity with square equal to zero. I denote the universal algebra generated by taking all sums and products of null vectors over the real or complex numbers by N. The rules of addition and multiplication in N…
During the last decades algebraization of space turned out to be a promising tool at the interface between Mathematics and Theoretical Physics. Starting with works by Gel'fand-Kolmogoroff and Gel'fand-Naimark, this branch developed as from…
A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centraliser of this action a quantum algebra (a quasi-triangular Hopf algebra) U_q with a representation…
We consider the gauge algebra of closed string field theory with a focus on diffeomorphisms. This algebra contains off-shell information in two ways. The first way is geometric, through the choice of three-punctured sphere defining the…
The moduli space of Anosov representations of a surface group in a semisimple group, which is an open set in the character variety, admits many more natural functions than the regular functions. We will study in particular length functions…
This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…
We give an elementary proof of isomorphism of the blob (diagram) algebra and the corresponding extended Temperley-Lieb algebra (defined by presentation).
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 consider GL$_m$-dimers of triangulations of regular convex $n$-gons, which give rise to a dimer model with boundary $Q$ and a dimer algebra $\Lambda_Q$. Let $e_b$ be the sum of the idempotents of all the boundary vertices, and…