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The Poincaré group as a Drinfel’d double - MaRDI portal

The Poincaré group as a Drinfel’d double (Q3383567)

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Language	Label	Description	Also known as
English	The Poincaré group as a Drinfel’d double	scientific article

Statements

scholarly article

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The Poincaré group as a Drinfel’d double (English)

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Classical and Quantum Gravity

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publication date

24 September 2021

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full work available at URL

https://arxiv.org/abs/1809.09207

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zbMATH Keywords

Poincaré group

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Drinfel'd double

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Lie bialgebra

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noncommutative spacetime

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(2 + 1)-gravity

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cosmological constant

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Ángel Ballesteros

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Ivan Gutierrez-Sagredo

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Francisco J. Herranz

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MaRDI profile type

MaRDI publication profile

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State sum invariants of 3-manifolds and quantum \(6j\)-symbols

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Combinatorial quantization of the Hamiltonian Chern-Simons theory. I

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Combinatorial quantization of the Hamiltonian Chern-Simons theory. II

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Representation theory of Chern-Simons observables

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Two dimensional lattice gauge theory based on a quantum group

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The quantisation of Poisson structures arising in Chern-Simons theory with gauge group \(G\ltimes{\mathfrak g}^*\)

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Cosmological deformation of Lorentzian spin foam models

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Quantum deformation of two four-dimensional spin foam models

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Hopf algebras for physics at the Planck scale

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New quantum Poincaré algebra and \(\kappa\)-deformed field theory

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A new ``null-plane'' quantum Poincaré algebra

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A non-commutative Minkowskian spacetime from a quantum AdS algebra

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DOUBLY SPECIAL RELATIVITY VERSUS κ-DEFORMATION OF RELATIVISTIC KINEMATICS

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Relative locality in κ-Poincaré

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Curved momentum spaces from quantum groups with cosmological constant

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\(2+1\)-dimensional gravity as an exactly soluble system

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Symplectic structure of the moduli space of flat connection on a Riemann surface

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Quantum symmetry, the cosmological constant and Planck-scale phenomenology

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Generalised Chern-Simons actions for 3d gravity and \(\kappa \)-Poincaré symmetry

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<i>q</i>-deformation and semidualization in 3D quantum gravity

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Physical constraints on quantum deformations of spacetime symmetries

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Quantum deformation of Lorentz group

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Topological field theory and the quantum double of \(\text{SU}(2)\)

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Hamiltonian quantization of Chern Simons theory with <i>SL</i> (2, ) group

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The Hilbert space of 3d gravity: quantum group symmetries and observables

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Quaternionic and Poisson–Lie structures in three-dimensional gravity: The cosmological constant as deformation parameter

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Drinfel'd doubles for (2+1)-gravity

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A \((2+1)\) non-commutative Drinfel'd double spacetime with cosmological constant

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Twisted \((2+1)\) \(\kappa\)-AdS algebra, Drinfel'd doubles and non-commutative spacetimes

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Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

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Quantum homogeneous spaces, duality and quantum 2-spheres

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AdS Poisson homogeneous spaces and Drinfel’d doubles

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Classification of three-dimensional Lie bialgebras

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CLASSIFICATION OF SIX-DIMENSIONAL REAL DRINFELD DOUBLES

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Quantum group symmetry and particle scattering in \((2+1)\)-dimensional quantum gravity

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Quantum mechanics of a point particle in -dimensional gravity

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Noncommutative geometry of angular momentum space U(su(2))

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Noncommutative model with spontaneous time generation and Planckian bound

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Three dimensional quantum geometry and deformed symmetry

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Poisson-Lie structures on Poincaré and Euclidean groups in three dimensions

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Kinematical Lie algebras via deformation theory

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Poisson structure and symmetry in the Chern–Simons formulation of (2 1)-dimensional gravity

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Classical <i>r</i> -matrices for the generalised Chern–Simons formulation of 3d gravity

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On Poisson homogeneous spaces of Poisson-Lie groups

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Poisson structures on Poincaré group

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New Lie-algebraic and quadratic deformations of Minkowski space from twisted Poincaré symmetries

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Quantum (2+1) kinematical algebras: a global approach

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Quantum deformations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \(\mathfrak{o}^\star(4)\) symmetries in unified \(\mathfrak{o}(4; \mathbb{C})\) setting

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Addendum to: ``Quantum deformations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \(\mathfrak{o}^\star(4)\) symmetries in unified \(\mathfrak{o}(4; \mathbb{C})\) setting''

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Wess-Zumino-Witten model based on a nonsemisimple group

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Poincaré gauge theory for gravitational forces in (1+1) dimensions

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Quantization of Drinfel'd doubles

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CLASSIFICATION OF POISSON–LIE T-DUAL MODELS WITH TWO-DIMENSIONAL TARGETS

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Non-standard quantum (1+1) Poincare group: a T-matrix approach

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Null-plane quantum universal \(R\)-matrix

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Kinematical lie algebras in 2 + 1 dimensions

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From Lorentzian to Galilean (2+1) gravity: Drinfelʼd doubles, quantization and noncommutative spacetimes

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Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

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Towards \((3+1)\) gravity through Drinfel'd doubles with cosmological constant

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The \(\kappa\)-(A)dS quantum algebra in \((3+1)\) dimensions

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Higher-dimensional kinematical Lie algebras via deformation theory

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\(SU(2)\) Poisson-Lie \(T\) duality

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Poisson-Lie \(T\)-duality and Bianchi type algebras

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Poisson-Lie \(T\)-duality for quasitriangular Lie bialgebras

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1088/1361-6382/AAF3C2

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Sitelinks

Mathematics(1 entry)

mardi Publication:3383567

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