Related papers: Modular Double of Quantum Group
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
Framed quiver moduli parametrize stable pairs consisting of a quiver representation and a map to a fixed graded vector space. Geometric properties and explicit realizations of framed quiver moduli for quivers without oriented cycles are…
A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An…
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to…
We discuss a generalization of the quantum group $\su$ to the $q$-Virasoro algebra in two-dimensional electrons system under uniform magnetic field. It is shown that the integral representations of both algebras are reduced to those in a…
From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.
A recently proposed renormalization group approach to dimensional crossover in quasi-one-dimensional quantum antiferromagnets is improved and then shown to give identical results, in some cases, to those obtained earlier.
We develop an elementary divisor theory for the unimodular and the modular group over quadratic field extensions and quaternion algebras. In particular, we investigate which sets of elementary divisors can occur. Under an additional…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…
The purpose of this paper is to consider some basic constructions in the category of compact quantum groups --for example de case of extensions, of Drinfeld twists, of matched pairs, of extensions, of linked pairs and of cocycle Singer…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
We give a parametrization of the canonical basis of the modified quantum group corresponding to a root datum in terms of the flag manifold over the semifield Z associated to the reductive group corresponding to the dual root datum. Some…
In this paper the q-deformed $W$ algebra $\WW_q$ is constructed, whose nontrivial quantum group structure is presented.
The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents…
We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express…
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
By encoding a qudit in a harmonic oscillator and investigating the d --> infinity limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators…
We prove a general theorem for constructing integral quantum cluster algebras over ${\mathbb{Z}}[q^{\pm 1/2}]$, namely that under mild conditions the integral forms of quantum nilpotent algebras always possess integral quantum cluster…