Related papers: Gerbes on quantum groups
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
Quantum groups have been widely explored as a tool to encode possible nontrivial generalisations of reference frame transformations, relevant in quantum gravity. In quantum information, it was found that the reference frames can be…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
We find two different q-generalizations of Yang-Mills theories. The corresponding lagrangians are invariant under the q-analogue of infinitesimal gauge transformations. We explicitly give the lagrangian and the transformation rules for the…
The q-deformed coherent states for a quantum particle on a circle are introduced and their properties investigated.
We complete the classification of quantum subgroups of $SL_q(2)$ with $q$ a root of unity of arbitrary order, that is, Hopf algebra quotients of the quantum function algebras $\mathcal{O}_{q} (SL_2(\mathbb{C}))$.
The Verma modules over the quantum groups $\mathrm U_q(\mathfrak{gl}_{l + 1})$ for arbitrary values of $l$ are analysed. The explicit expressions for the action of the generators on the elements of the natural basis are obtained. The…
We construct a family of q-deformations of SU(2) for complex parameters q not equal to 0. For real q, the deformation coincides with Woronowicz' compact quantum SU_q(2) group. For q not real, SU_q(2) is only a braided compact quantum group…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
The concept of a quantum algebra is made easy through the investigation of the prototype algebras $u_{qp}(2)$, $su_q(2)$ and $u_{qp}(1,1)$. The latter quantum algebras are introduced as deformations of the corresponding Lie algebras~; this…
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…
We investigate the algebro-geometric structure of a novel two-parameter quantum deformation which exhibits the nature of a semidirect or cross-product algebra built upon GL(2) x GL(1), and is related to several other known examples of…
We present a group of transformations in the space of generalized connections that contains the set of transformations generated by the flux variables of loop quantum gravity. This group is labelled by certain SU(2)-valued functions on the…
The quantum group structure of the Liouville theory is reviewd and shown to be an important tool for solving the theory.
We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on $SU_q(2)$ . The…
In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules.
Firstly we discuss different versions of noncommutative space-time and corresponding appearance of quantum space-time groups. Further we consider the relation between quantum deformations of relativistic symmetries and so-called doubly…
When the $q$-deformed creation and annihilation operators are used in a second quantization procedure, the algebra satisfied by basis vectors (orthogonal complete set) should be also deformed such as a field operator remains invariant under…
Quantum de Rham complexes on the quantum plane and the quantum group itself are constructed for the Zakrewski deformation of $ Fun ( SL(2)) $. As a by-product a new deformation of the two dimensional Heisenberg algeb ra is constructed which…
The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL$(1| 1)$ via a contraction of GL$_{p,q}(1| 1)$ is presented. Related differential calculus on the quantum superplane is introduced.