Related papers: Kappa-Deformations: Historical Developments and Re…
Unified graded differential algebra, generated by $\kappa$-Minkowski noncommutative (NC) coordinates, Lorentz generators and anticommuting one-forms, is constructed. It is compatible with $\kappa$-Poincar\'e-Hopf algebra. For time- and…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
We present a short review describing the use of noncommutative space-time in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their…
We present the quantum $\kappa$-deformation of BMS symmetry, by generalizing the lightlike $\kappa$-Poincar\'e Hopf algebra. On the technical level, our analysis relies on the fact that the lightlike $\kappa$-deformation of Poincar\'e…
The Yang algebra was proposed a long time ago as a generalization of the Snyder algebra to the case of curved background spacetime. It includes as subalgebras both the Snyder and the de Sitter algebras and can therefore be viewed as a model…
We construct discrete versions of $\kappa$-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical…
In this paper we provide universal formulas describing Drinfeld-type quantization of inhomogeneous orthogonal groups determined by a metric tensor of an arbitrary signature living in a spacetime of arbitrary dimension. The metric tensor…
In this note we present an approach using both constructive and Hopf algebraic methods to contribute to the not yet fully satisfactory definition of an integral on kappa-deformed spacetime. The integral presented here is based on the inner…
A spacetime interpretation of deformed relativity symmetry groups was recently proposed by resorting to Finslerian geometries, seen as the outcome of a continuous limit endowed with first order corrections from the quantum gravity regime.…
In this short review of Doubly Special Relativity I describe first the relations between DSR and (quantum) gravity. Then I show how, in the case of a field theory with curved momentum space, the Hopf algebra of symmetries naturally emerges.…
The doubly special relativity (DSR) theories are suggested in order to incorporate an observer-independent length scale in special theory of relativity. The Magueijo-Smolin proposal of DSR is realizable through a particular form of the…
We calculate the first supersymmetric and kappa-symmetric derivative deformation of the M5-brane worldvolume theory in a flat eleven-dimensional background. By applying cohomological techniques we obtain a deformation of the standard…
We propose canonical and Lie-algebraic twist deformations of $\kappa$-deformed Poincare Hopf algebra which leads to the generalized $\kappa$-Minkowski space-time relations. The corresponding deformed $\kappa$-Poincare quantum groups are…
Recent work showed that $\kappa$-deformations can describe the quantum deformation of several relativistic models that have been proposed in the context of quantum gravity phenomenology. Starting from the Poincar\'e algebra of…
We consider two new classes of twisted D=4 quantum Poincar\'{e} symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincar\'{e} algebras which provide the…
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…
In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length. The classical and quantum dynamics of a…
The classical $r$-matrix for $N=1$ superPoincar{\'e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{\'e} supergroup. The standard correspondence principle between the…
The kappa-deformed dual pair of Poincare algebra and Poincare group is formulated in the framework of Heisenberg doubles. The covariant kappa-deformed phase space is described in detail as a subalgebra.The realizations of proposed algebraic…
We study the deformed AdS_5 x S^5 supercoset model of arXiv:1309.5850 which depends on one parameter kappa and has classical quantum group symmetry. We confirm the conjecture that in the "maximal" deformation limit kappa -> infinity this…