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The eight nonisomorphic Drinfel'd double (DD) structures for the Poincar\'e Lie group in (2+1) dimensions are explicitly constructed in the kinematical basis.
Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations
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Three-dimensional Einstein gravity: dynamics of flat space
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A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories
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Quantum Groups
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Hopf algebras for physics at the Planck scale
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2+1 dimensional gravity as an exactly soluble system
E. Witten · 1988
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Quantum deformation of Lorentz group
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q-deformation of Poincaré algebra
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State sum invariants of 3-manifolds and quantum 6j-symbols
V. G. Turaev and O. Y. Viro · 1992
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New quantum Poincaré algebra and κ \kappa -deformed field theory
J. Lukierski, A. Nowicki, and H. Ruegg · 1992
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On Poisson homogeneous spaces of Poisson-Lie groups
V. Drinfeld · 1993
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Wess-Zumino-Witten model based on a nonsemisimple group
C. R. Nappi and E. Witten · 1993
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Poincaré gauge theory for gravitational forces in (1+1) dimensions
D. Cangemi and R. Jackiw · 1993
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Quantum homogeneous spaces, duality and quantum 2-spheres
M. S. Dijkhuizen and T. H. Koornwinder · 1994
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A guide to Quantum Groups
V. Chari and A. Pressley · 1994
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Quantum (2+1) kinematical algebras: a global approach
A. Ballesteros, F. J. Herranz, M. A. del Olmo, and M. Santander · 1994
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Combinatorial quantization of the Hamiltonian Chern-Simons theory I
A. Y. Alekseev, H. Grosse, and V. Schomerus · 1995
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Two dimensional lattice gauge theory based on a quantum group
E. Buffenoir and P. Roche · 1995
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A new “null-plane” quantum Poincaré algebra
A. Ballesteros, F. J. Herranz, M. A. del Olmo, and M. Santander · 1995
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Symplectic structure of the moduli space of flat connection on a Riemann surface
A. Y. Alekseev and A. Z. Malkin · 1995
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Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras
A. Ballesteros, N. A. Gromov, F. J. Herranz, M. A. del Olmo, and M. Santander · 1995
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Non-standard quantum (1+1) Poincare group: a T-matrix approach
A. Ballesteros, F. J. Herranz, M. A. del Olmo, C. M. Pereña, and M. Santander · 1995
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Dual non-Abelian duality and the Drinfeld double
C. Klimčík and P. Ševera · 1995
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Combinatorial quantization of the Hamiltonian Chern-Simons theory II
A. Y. Alekseev, H. Grosse, and V. Schomerus · 1996
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Representation theory of Chern-Simons observables
A. Y. Alekseev and V. Schomerus · 1996
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Poisson Structures on the Poincaré Group
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Null-plane quantum universal R-matrix
A. Ballesteros, F. J. Herranz, and C. M. Pereña · 1997
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Quantum gravity in 2+ 1 dimensions
S. Carlip · 1998
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Topological field theory and the quantum double of SU(2)
F. A. Bais and N. M. Muller · 1998
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Quantum mechanics of a point particle in (2+1)-dimensional gravity
H.-J. Matschull and M. Welling · 1998
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Poisson-Lie structures on Poincaré and Euclidean groups in three dimensions
P. Stachura · 1998
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Poisson-Lie T-duality beyond the classical level and the renormalization group
K. Sfetsos · 1998
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SU(2) Poisson-Lie T duality
M. A. Lledó and V. S. Varadarajan · 1998
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Poisson structure on moduli of flat connections on Riemann surfaces and r-matrix
V. V. Fock and A. A. Rosly · 1999
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q -deformation and semidualization in 3D quantum gravity
S. Majid and B. J. Schroers · 2009
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Three dimensional quantum geometry and deformed Poincaré symmetry
E. Joung, J. Mourad, and K. Noui · 2009
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A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
G. Papageorgiou and B. J. Schroers · 2009
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Doubly-special relativity: Facts, myths and some key open issues
G. Amelino-Camelia · 2010
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The Hilbert space of 3d gravity: quantum group symmetries and observables
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Poisson-Lie T-duality and Bianchi type algebras
M. A. Jafarizadeh and A. Rezaei-Aghdam · 1999
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Classification of three-dimensional Lie bialgebras
X. Gomez · 2000
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Poisson-Lie T-duality for quasitriangular Lie bialgebras
E. J. Beggs and S. Majid · 2001
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Hamiltonian quantization of Chern-Simons theory with SL(2,R) group
E. Buffenoir, K. Noui, and P. Roche · 2002
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Classification of 6-dimensional real Drinfeld doubles
L. Snobl and L. Hlavaty · 2002
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Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity
F. A. Bais, N. M. Muller, and B. J. Schroers · 2002
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C. Meusburger and K. Noui · 2010
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Three-dimensional gravity and Drinfel’d doubles: Spacetimes and symmetries from quantum deformations
A. Ballesteros, F. J. Herranz, and C. Meusburger · 2010
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Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
G. Papageorgiou and B. J. Schroers · 2010
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Quantum deformation of two four-dimensional spin foam models
W. J. Fairbairn and C. Meusburger · 2012
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Living in curved momentum space
J. Kowalski-Glikman · 2013
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Relative locality in κ \kappa -Poincaré
G. Gubitosi and F. Mercati · 2013
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Drinfel’d doubles for (2+1)-gravity
A. Ballesteros, F. J. Herranz, and C. Meusburger · 2013
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On quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions
A. Ballesteros, F. J. Herranz, and F. Musso · 2014
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A (2 + 1) non-commutative Drinfel’d double spacetime with cosmological constant
A. Ballesteros, F. J. Herranz, and C. Meusburger · 2014
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Twisted (2+1) κ \kappa -AdS algebra, Drinfel’d doubles and non-commutative spacetimes
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A. Ballesteros, F. J. Herranz, and P. Naranjo · 2014
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Towards (3+1) gravity through Drinfel’d doubles with cosmological constant
A. Ballesteros, F. J. Herranz, and P. Naranjo · 2015
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Curved momentum spaces from quantum groups with cosmological constant
A. Ballesteros, G. Gubitosi, I. Gutiérrez-Sagredo, and F. J. Herranz · 2017
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Quantum groups and noncommutative spacetimes with cosmological constant
A. Ballesteros, I. Gutiérrez-Sagredo, F. J. Herranz, C. Meusburger, and P. Naranjo · 2017
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AdS Poisson homogeneous spaces and Drinfel’d doubles
A. Ballesteros, C. Meusburger, and P. Naranjo · 2017
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The κ \kappa -(A)dS quantum algebra in (3 + 1) dimensions
A. Ballesteros, F. J. Herranz, F. Musso, and P. Naranjo · 2017
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Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions
A. Ballesteros, G. Gubitosi, I. Gutiérrez-Sagredo, and F. J. Herranz · 2018
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Physical constraints on quantum deformations of spacetime symmetries
F. Mercati and M. Sergola · 2018
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Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries
A. Ballesteros and F. Mercati · 2018
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Kinematical Lie algebras via deformation theory
J. M. Figueroa-O’Farrill · 2018
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Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity
P. K. Osei and B. J. Schroers · 2018
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Kinematical Lie algebras in 2 + 1 dimensions
T. Andrzejewski and J. M. Figueroa-O’Farrill · 2018
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Higher-dimensional kinematical Lie algebras via deformation theory
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