Related papers: Fractional spin through quantum strange superalgeb…
We review the q-deformed spin network approach to topological quantum field theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the…
A argument is described for how deformed or doubly special relativity may arise in the semiclassical limit of a quantum theory of gravity. We consider a generic quantum theory of gravity coupled to matter, from which we use only the…
Several Clifford algebras that are covariant under the action of a Lie algebra $g$ can be deformed in a way consistent with the deformation of $Ug$ into a quantum group (or into a triangular Hopf algebra) $U_qg$, i.e. so as to remain…
In this paper, we introduce and study the quantum deformations of the cluster superalgebra. Then we prove the quantum version of the Laurent phenomenon for the super-case.
This is a short summary of the paper hep-th/9910037. An algebra of functions on q-deformed Anti-de Sitter space AdS_q^D is defined for q a root of unity, which is covariant under U_q(so(2,D-1)). The scalar fields have an intrinsic high-…
We propose a novel way of investigating the universal properties of spin systems by coupling them to an ensemble of causal dynamically triangulated lattices, instead of studying them on a fixed regular or random lattice. Somewhat…
We discuss the algebra of $N\times N$ matrices as a reduced quantum plane. A $3-$nilpotent deformed differential calculus involving a complex parameter $q$ is constructed. The two cases, $q$ $3^{rd}$ and $N^{th}$ root of unity are…
The quantum super-algebra structure on the deformed super Virasoro algebra is investigated. More specifically we established the possibility of defining a non trivial Hopf super-algebra on both one and two-parameters deformed super Virasoro…
Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well…
We discuss the second quantization of scalar field theory on the q-deformed fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find quantum field theories which are manifestly covariant under U_q(su(2)), have a smooth…
We introduce a notion of $Q$-algebra that can be considered as a generalization of the notion of $Q$-manifold (a supermanifold equipped with an odd vector field obeying $\{Q,Q\} =0$). We develop the theory of connections on modules over…
A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather…
Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are important from a physical point of view…
The aim of this paper is to give a complete classification of irreducible finite dimensional representations of the nonstandard q-deformation U'_q(so(n)) (which does not coincide with the Drinfeld-Jimbo quantum algebra U_q(so(n)) of the…
We explore in detail the role in euclidean 3d quantum gravity of quantum Born reciprocity or `semidualisation'. The latter is an algebraic operation defined using quantum group methods that interchanges position and momentum. Using this we…
The quantum superalgebra $U_q[gl(2/1)]$ is given as both a Drinfel'd--Jimbo deformation of $U[gl(2/1)]$ and a Hopf superalgebra. Finite--dimensional representations of this quantum superalgebra are constructed and investigated in a basis of…
We give a diagrammatic presentation of the category of $\textbf{U}_q(\mathfrak{sl}_2)$-tilting modules $\mathfrak{T}$ for $q$ being a root of unity and introduce a grading on $\mathfrak{T}$. This grading is a "root of unity phenomenon" and…
We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…
We show that the quantum coordinate ring of a semisimple group is a unique factorisation domain in the sense of Chatters and Jordan in the case where the deformation parameter q is a transcendental element.
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived.…