Related papers: Two-parameter extensions of the \kappa-Poincar\'{e…
The quantum duality principle is used to obtain explicitly the Poisson analogue of the kappa-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson-Lie structure on the dual solvable Lie group. The construction is fully…
We demonstrate that the coproduct of D=2 and D=4 quantum kappa-Poincare algebra in classical algebra basis can not be obtained by the cochain twist depending only on Poincare algebra generators. We also argue that nonexistence of such a…
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…
We introduce the notion of formal multiparameter quantum universal enveloping algebras - in short FoMpQUEA - as a straightforward generalization of Drinfeld's quantum group. Then we show that the class of FoMpQUEA's is closed under…
Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J_0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some…
The three quantum groups dual to the generalized twist deformed Poincare Hopf algebras are provided with use of FRT procedure. Their Galilean counterparts are obtained by nonrelativistic contraction scheme.
In this paper, we introduce non-standard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$,…
In this paper I would like to show how the Deformed Special Relativity family of models - developed to approach spacetime quantization - can actually be applied to the description of classical cosmology. I use the bicrossproduct basis of…
We present Lie-algebraic deformations of Minkowski space with undeformed Poincare algebra. These deformations interpolate between Snyder and kappa-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative…
We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a…
Usually, the realizations of the noncommutative Snyder model lead to a nonassociative star product. However, it has been shown that this problem can be avoided by adding to the spacetime coordinates new tensorial degrees of freedom. The…
The dimension of the third homogeneous component of a matrix quantum bialgebra, determined by pair of quantum spaces, is calculated. The Poincar\'{e} series of some deformations of $GL(n)$ is calculated. A new deformation of $GL(3)$ with…
We construct sets of structure matrices for the semi-dynamical reflection algebra, solving the Yang-Baxter type consistency equations extended by the action of an automorphism of the auxiliary space. These solutions are parametrized by…
We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten (WZNW) models at the classical level. The target space is given by squashed S^3 and the isometry is SU(2)_L x U(1)_R. It is known…
I shall recall in historical perspective some results from nineties and show further how $\kappa$-deformed symmetries and $\kappa$-Minkowski space inspired DSR (Doubly of Deformed Special Relativity) approach proposed after 2000. As very…
A quantization of a non-standard rational solution of CYBE for $sl_2$ is given explicitly. We obtain the quantization with the help of a twisting of the usual Yangian $Y(sl_2$. This quantum object (deformed Yangian $Y_{\eta,\xi}(sl_2))$ is…
Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is…
The general framework of bicrossproduct Hopf algebras given by Majid is extended to $Z_2$-graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the graded algebras of functions on undeformed…
In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of…
The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these…