Related papers: Large-scale quantization of trace I: Finite propag…
Inspired by factorized scattering from delta-type impurities in (1+1)-dimensional space-time, we propose and analyse a generalization of the Zamolodchikov-Faddeev algebra. Distinguished elements of the new algebra, called reflection and…
This paper is the continuation of the paper arXiv:1509.06950, which is Part I under the same title. In this paper, we prove a generalized Cauchy formula for the integrals of logarithmic forms on products of projective lines, and give an…
Generalized quons interpolating between Bose, Fermi, para-Bose, para-Fermi, and anyonic statistics are proposed. They follow from the R-matrix approach to deformed associative algebras. It is proved that generalized quons have the same main…
Khovanov-Lauda define a 2-category $\mathcal{U}$ such that the split Grothendieck group $K_0(\mathcal{U})$ is isomorphic to an integral version of the quantized universal enveloping algebra $\mathbf{U}(\mathfrak{sl}_n)$, $n \geq 2$.…
We describe the central measures for the random walk on graded graphs. Using this description, we obtain the list of all finite traces on three infinite-dimensional algebras: on the Brauer algebra, on the partition algebra, and on the…
Holonomy R-matrices parametrized by finite-dimensional representations are constructed for quantized universal enveloping algebras of simple Lie algebras at roots of 1.
John Roe \cite{Roe lectures} introduced coarse structures for arbitrary sets $X$ by considering subsets of $X\times X$. That definition, while natural for analysts, is a bit more difficult to digest for topologists and geometers. In this…
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
In this paper we consider all possible generalizations of the B-type Hecke algebras, namely the cyclotomic and what we call 'generalized', and we construct Markov traces on each of them, so as to obtain all possible different levels of…
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a…
While not obvious from its initial motivation in linear algebra, there are many context where iterated traces can be defined. In this paper we prove a very general theorem about iterated 2-categorical traces. We show that many…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
We determine the class of finite T_0-spaces allowing for a universal coefficient theorem computing equivariant KK-theory by filtrated K-theory.
We review the construction of generalized integrable hierarchies of partial differential equations, associated to affine Kac-Moody algebras, that include those considered by Drinfel'd and Sokolov. These hierarchies can be used to construct…
In this paper we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual…
It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…
The concept of generalized path algebras was introduced in (Coelho, Liu, 2000). Roughly speaking, these algebras are constructed in a similar way to that of the path algebras over a quiver, the difference being that we assign an algebra to…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…