Related papers: New quantum "az+b" groups
This article gives a brief introduction to $q$-special functions, i.e., $q$-analogues of the classical special functions. Here $q$ is a deformation parameter, usually $0<q<1$, where $q=1$ is the classical case. The main topics to be treated…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
A model of 3-dimensional topological quantum field theory is rigorously constructed. The results are applied to an explicit formula for deformation quantization of any finite-dimensional Lie bialgebra over the field of complex numbers. This…
The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
Quantum groups and quantum algebras have received considerable attention in the last decades because they are very useful as mathematical tools of research. Existing proposals for quantum groups have always suggested the idea of deforming a…
In this paper, we first discuss cohomology and a one-parameter formal deformation theory of Lie-Yamaguti algebras. Next, we study finite group actions on Lie-Yamaguti algebras and introduce equivariant cohomology for Lie-Yamaguti algebras…
Representation learning seeks meaningful sensory representations without supervision and can model aspects of human development. Although many neural networks empirically learn useful features, a principled account of what makes a…
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…
A new derivation of the quantum deformation of the 2 dimensional Euclidean Poincare group (cf S. Zakrzewski) is proposed. It is based on a contraction of the Hopf algebra Fun(SO_q(3)). The deformation parameter q is sent to one, as in the…
The quantum algebra suq(2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of $q$-bosons. In connection with the quantum algebra suq(2), we discuss the q-analogues of the…
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…
We construct some braided quantum groups over the circle group. These are analogous to the free orthogonal quantum groups and generalise the braided quantum SU(2) groups for complex deformation parameter. We describe their irreducible…
Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…
This work deals with scalar field theories and supersymmetric quantum mechanics. The investigation is inspired by a recent result, which shows how to use the reconstruction mechanism to describe two distinct field theories from the very…