相关论文: Towards new relativistic doubly $\kappa$-deformed …

Recently it was shown that by using two different realizations of $\hat{o}(1,4)$ Lie algebra one can describe one-parameter standard Snyder model and two-parameter $\kappa$-deformed Snyder model. In this paper, by using the generalized Born…

We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase space as given by Heisenberg double \mathcal{H} of D=4 kappa-deformed Poincare-Hopf algebra H. The standard (4+4) -dimensional kappa - deformed covariant quantum…

We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…

We propose the doubly $\kappa$-dependent Yang quantum phase space which describes the generalization of $D = 4$ Yang model. We postulate that such model is covariant under the generalized Born map, what permits to derive this new model from…

We deform Heisenberg algebra and corresponding coalgebra by twist. We present undeformed and deformed tensor identities. Coalgebras for the generalized Poincar\'{e} algebras have been constructed. The exact universal $R$-matrix for the…

We describe the deformed covariant phase space corresponding to the so-called kappa-deformation of D=4 relativistic symmetries, with quantum ``time'' coordinate and Heisenberg algebra obtained according to the Heisenberg double…

We describe, in an algebraic way, the $\kappa$-deformed extended Snyder models, that depend on three parameters $\beta, \kappa$ and $\lambda$, which in a suitable algebra basis are described by the de Sitter algebras ${o}(1,N)$. The…

The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…

The $(4+4)$-dimensional $\kappa$-deformed quantum phase space as well as its $(10+10)$-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the $(10+10)$-dimensional quantum phase space is the double…

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…

We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory - the Poincar\'{e} symmetries. The most complete way of introducing the modifications is via the noncocommutative…

We consider $\kappa$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincar\'e algebra is unaltered,…

We propose a new Doubly Special Relativity theory based on the generalization of the $\kappa$-deformation of the Poincar\'e algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincar\'e…

We consider the extensions of classical r-matrix for \kappa-deformed Poincar\'{e} algebra which satisfy modified Yang-Baxter equation. Two examples introducing additional deformation parameter (dimensionfull \frac{1}{\widetilde{\kappa}} or…

We consider two quantum phase spaces which can be described by two Hopf algebroids linked with the well-known $\theta_{\mu \nu }$-deformed $D=4$ Poincare-Hopf algebra $\mathbb{H}$. The first algebroid describes $\theta_{\mu \nu }$-deformed…

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 provide first explicite examples of quantum deformations of D=4 conformal algebra with mass-like deformation parameters, in applications to quantum gravity effects related with Planck mass. It is shown that one of the classical…

We present two different quantum deformations for the (anti)de Sitter algebras and groups. The former is a non-standard (triangular) deformation of SO(4,2) realized as the conformal group of the (3+1)D Minkowskian spacetime, while the…

The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The $\kappa$-deformed phase space with noncommutative coordinates is realized in terms of undeformed quantum phase space. There are…

We twist the Hopf algebra of igl(n,R) to obtain the kappa-deformed spacetime coordinates. Coproducts of the twisted Hopf algebras are explicitly given. The kappa-deformed spacetime obtained this way satisfies the same commutation relation…