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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.…

High Energy Physics - Theory · Physics 2017-11-29 Angel Ballesteros , N. Rossano Bruno , Francisco J. Herranz

The $\hat\kappa$-deformed extended Galilei Hopf group algebra, ${\rm Fun}_{\hat\kappa}(\tilde G_{(m)})$, is introduced. It provides an example of a cocycle bicrossproduct structure, and is shown to be the contraction limit of a…

q-alg · Mathematics 2008-11-26 J. A. de Azcarraga , J. C. Perez Bueno

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.…

General Relativity and Quantum Cosmology · Physics 2017-02-22 Marco Letizia , Stefano Liberati

We discuss how the symmetries of $\kappa$-Minkowski non-commutative spacetime can be described by the $\kappa$-Poincar\'e Hopf algebra. In particular, we focus on a generalization of the Noether analysis in the $\kappa$-deformed framework…

High Energy Physics - Theory · Physics 2008-11-26 Michele Arzano

It is often expected that one cannot treat spacetime as a continuous manifold as the Planck scale is approached, because of to possible effects due to a quantum theory of gravity. There have been several proposals to model such a deviation…

General Relativity and Quantum Cosmology · Physics 2023-01-23 Andrea Bevilacqua

A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This…

High Energy Physics - Theory · Physics 2008-11-26 Marija Dimitrijevic , Larisa Jonke , Lutz Möller , Efrossini Tsouchnika , Julius Wess , Michael Wohlgenannt

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…

High Energy Physics - Theory · Physics 2019-02-06 A. Borowiec , L. Brocki , J. Kowalski-Glikman , J. Unger

In the following work we will introduce and discuss in detail a particular model of complex $\kappa$-deformed scalar field, whose behaviour under C, P , T transformation is particularly transparent from both a formal and phenomenological…

High Energy Physics - Theory · Physics 2023-11-02 Andrea Bevilacqua

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…

High Energy Physics - Theory · Physics 2008-11-26 Jong-Geon Bu , Hyeong-Chan Kim , Youngone Lee , Chang Hyon Vac , Jae Hyung Yee

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…

High Energy Physics - Theory · Physics 2009-11-10 A. Blaut , M. Daszkiewicz , J. Kowalski-Glikman

Given a Heisenberg algebra A of canonical commutation relations modelled over an infinite-dimensional nuclear space, a Hopf algebra of its quantum deformations is also an algebra of canonical commutation relations whose Fock representation…

Quantum Physics · Physics 2007-05-23 G. Sardanashvily

Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both…

High Energy Physics - Theory · Physics 2018-05-29 Niels G. Gresnigt , Adam B. Gillard

Two one-parameter families of twists providing kappa-Minkowski * -product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module…

Mathematical Physics · Physics 2009-06-30 A. Borowiec , A. Pachol

We extend our previous study of Hopf-algebraic $\kappa$-deformations of all inhomogeneous orthogonal Lie algebras ${\rm iso}(g)$ as written in a tensorial and unified form. Such deformations are determined by a vector $\tau$ which for…

Mathematical Physics · Physics 2014-12-02 Andrzej Borowiec , Anna Pachol

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…

High Energy Physics - Theory · Physics 2009-11-11 J. Lukierski , M. Woronowicz

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…

High Energy Physics - Theory · Physics 2010-04-30 S. Meljanac , D. Meljanac , A. Samsarov , M. Stojic

We propose a contraction of the de Sitter quantum group leading to the quantum Poincare group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non--commutative space, and the deformation parameter $q$…

High Energy Physics - Theory · Physics 2009-10-28 Philippe Zaugg

In this paper, using a Hopf-algebraic method, we construct deformed Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can see the…

High Energy Physics - Theory · Physics 2009-11-10 Yoshishige Kobayashi , Shin Sasaki

Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $\kappa$-Poincar\'e $T$-matrix is explicitly worked out.…

Quantum Algebra · Mathematics 2026-04-23 Angel Ballesteros , Diego Fernandez-Silvestre , Ivan Gutierrez-Sagredo

We study Lie algebra $\kappa$-deformed Euclidean space with undeformed rotation algebra $SO_a(n)$ and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are constructed and a corresponding star…

High Energy Physics - Theory · Physics 2009-01-07 Stjepan Meljanac , Marko Stojic