Related papers: $(\ell,p)$-Jones-Wenzl Idempotents
We show that the homology of any Temperley-Lieb algebra $\mathcal{TL}_n(a)$ on an odd number of strands vanishes in positive degrees. This improves a result obtained by Boyd-Hepworth. In addition we present alternative arguments for the…
We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and…
We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or…
We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a…
For an acyclic quiver Q, we solve the Clebsch-Gordan problem for the projective representations by computing the multiplicity of a given indecomposable projective in the tensor product of two indecomposable projectives. Motivated by this…
We introduce a new basis of the Temperley-Lieb algebra. It is defined using a bijection between noncrossing partitions and fully commutative elements together with a basis introduced by Zinno, which is obtained by mapping the simple…
Trivalent plane graphs are used in various areas of mathematics which relate for instance to the colored Jones polynomial, invariants of 3-manifolds and quantum computation. Their evaluation is based on computations in the Temperley-Lieb…
We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, $\pi$-regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and…
Over a finite-dimensonal algbera $A$, simple $A$-modules that have projective dimension one have special properties. For example, Geigle-Lenzing studied them in connection to homological epimorphisms of rings, and they have also appeared in…
We investigate properties of the group inverse in rings with unit related to products and differences of idempotents, and thus we extend some results from \cite{DENG} to more general settings. We show that most part of \cite{DENG} is easily…
Given a subfactor planar algebra P and a Hilbert P-module of lowest weight 0 we build a bimodule over the symmetric enveloping inclusion associated to P. As an application we prove diagrammatically that the Temperley-Lieb-Jones standard…
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…
We systematically study those rings whose non-units are a sum of an idempotent and a nilpotent. Some crucial characteristic properties are completely described as well as some structural results for this class of rings are obtained. This…
The purpose of this paper is to introduce basic concepts that are fundamental in the examination of composite moduli, while avoiding the notoriously difficult problem of prime-factorization. We introduce a new class of numbers, called…
We define a monoidal category $\operatorname{\mathbf{W}}$ and a closely related 2-category $\operatorname{\mathbf{2Weyl}}$ using diagrammatic methods. We show that $\operatorname{\mathbf{2Weyl}}$ acts on the category $\mathbf{TL}…
We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore,…
Let $G$ be a simple algebraic group over an algebraically closed field $k$ of characteristic $p$. The classification of the conjugacy classes of unipotent elements of $G(k)$ and nilpotent orbits of $G$ on $\operatorname{Lie}(G)$ is…
Let Q be a Dynkin quiver, and let P(Q) be the corresponding preprojective algebra. Let I be a set of pairwise different indecomposable irreducible components of varieties of P(Q)-modules such that generically there are no extensions between…
In this note we describe conditions under which, in idempotent functional analysis, linear operators have integral representations in terms of idempotent integral of V. P. Maslov. We define the notion of nuclear idempotent semimodule and…
In order to study the properties of SEP elements, we propose the concepts of one sided a_idempotent and one sided a_equivalent. Under the condition that an element in a ring is both group invertible and MP_invertible, some equivalent…