相关论文: Projectors in the Virtual Temperley-Lieb Algebra
We consider generalized inverses of linear operators on arbitrary vector spaces and study the question when their product in reverse order is again a generalized inverse. This problem is equivalent to the question when the product of two…
Jones and Penneys showed that a finite depth subfactor planar algebra embeds in the bipartite graph planar algebra of its principal graph, via a Markov towers of algebras approach. We relate several equivalent perspectives on the notion of…
We describe the cell structure of the affine Temperley-Lieb algebra with respect to a monomial basis. We construct a diagram calculus for this algebra.
We show that there is a unique Markov trace on the tower of Temperley--Lieb type quotients of Hecke algebras of Coxeter type $E_n$ (for all $n \geq 6$). We explain in detail how this trace may be computed easily using tom Dieck's calculus…
We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…
The basic properties of the Temperley-Lieb algebra $TL_n$ with parameter $\beta = q + q^{-1}$, for $q$ any non-zero complex number, are reviewed in a pedagogical way. The link and standard (cell) modules that appear in numerous physical…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
In the paper "Is there a Jordan geometry underlying quantum physics?" (Int. J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum…
The algebraic classification of the Weyl tensor in arbitrary dimension n is recovered by means of the principal directions of its "superenergy" tensor. This point of view can be helpful in order to compute the Weyl aligned null directions…
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…
A proto-quantum space is a (general) matricially normed space in the sense of Effros and Ruan presented in a `matrix-free' language. We show that these spaces have a special (projective) tensor product possessing the universal property with…
A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.
In this paper, we define a quotient of the cyclotomic Hecke algebra of type $G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and $B$. We establish a graded cellular structure for the generalised Temperley-Lieb…
We give an explicit set of generators for the semigroup of the Gr\"obner degeneration of a toric ideal. This set of generators is used to study algebraic properties of the semigroup it generates: approximation of semigroups,…
We develop the theory of relative monads and relative adjunctions in a virtual equipment, extending the theory of monads and adjunctions in a 2-category. The theory of relative comonads and relative coadjunctions follows by duality. While…
For C a factorisable and pivotal finite tensor category over an algebraically closed field of characteristic zero we show: 1) C always contains a simple projective object; 2) if C is in addition ribbon, the internal characters of projective…
The present thesis represents developments in two main directions related to the simple Lie algebras. The first one is devoted to the representation theory of the simple Lie algebras. Specifically, we present recent results, which include…
We give an overview of the question: which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive…
Given an abelian category, we introduce a categorical concept of (strongly) Gorenstein projective (resp., injective) objects, by defining a new special class of objects. Then we study the transfer of these properties when passing to an…