Related papers: $\kappa$-deformed BMS symmetry
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on \emph{commutative} manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter…
We introduce a multi-parameter twisted Hopf algebra associated with a root datum and show that its modified form is isomorphic to Lusztig's modified quantum algebra under certain restrictions on the parameters. By taking various…
To speak about identical particles - bosons or fermions - in quantum field theories with kappa-deformed Poincare symmetry, one must have a kappa-covariant notion of particle exchange. This means constructing intertwiners of the relevant…
A generalized Hopf algebra structure for the positive (negative) part of the Drinfeld-Jimbo quantum group of type A_n is established without make any use of the usual deformation of the abelian part of sl_{n+1}.
In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one existing in the literature, and therefore…
We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical…
By the supersymmetrization of a simple algebraic technique proposed in \cite{LuTo2017} we obtain the complete classification of all basic (nonisomorphic) quantum deformations for the orthosymplectic Lie superalgebra…
The possible description of the vacuum of quantum gravity through the so called kappa--Poincare group is analyzed considering some of the consequences of this symmetry in the path integral formulation of nonrelativistic quantum theory. This…
The $C^*$-algebraic $\kappa$-Poincar\'{e} Group is constructed. The construction uses groupoid algebras of differential groupoids associated to Lie group decomposition. It turns out the underlying $C^*$-algebra is the same as for…
We use factorisations of the local isometry groups arising in 3d gravity for Lorentzian and Euclidean signatures and any value of the cosmological constant to construct associated bicrossproduct quantum groups via semidualisation. In this…
Noncommutative spaces of geodesics provide an alternative way of introducing noncommutative relativistic kinematics endowed with quantum group symmetry. In this paper we present explicitly the seven noncommutative spaces of time-, space-…
We consider $\kappa$-deformed relativistic symmetries described algebraically by modified Majid-Ruegg bicrossproduct basis and investigate the quantization of field oscillators for the $\kappa$-deformed free scalar fields on…
We show that infinite variety of Poincar\'{e} bialgebras with nontrivial classical r-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the Poincar\'{e} bialgebras to…
The connection between braided Hopf algebra structure and the quantum group covariance of deformed oscillators is constructed explicitly. In this context we provide deformations of the Hopf algebra of functions on SU(1,1). Quantum subgroups…
We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a $\kappa$-deformed scalar…
We show that the effective dynamics of matter fields coupled to 3d quantum gravity is described after integration over the gravitational degrees of freedom by a braided non-commutative quantum field theory symmetric under a…
We show that the crossed modules and bicovariant different calculi on two Hopf algebras related by a cocycle twist are in 1-1 correspondence. In particular, for quantum groups which are cocycle deformation-quantisations of classical groups…
The positive and negative energy modes of a field theory in $\kappa$-Minkowski/$\kappa$-Poincar\'e noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two…
For a Poisson algebra $A$, by exploring its relation with Lie-Rinehart algebras, we prove a Poincar\'e-Birkoff-Witt theorem for its universal enveloping algebra $A^e$. Some general properties of the universal enveloping algebras of Poisson…
Replacing the continuous space by a cubic lattice we find a deformation of the Poincar\'e algebra. A deformation of the relativistic mass operator is shown to be a Casimir of the algebra. The real structure is preserved.