Basic quantizations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \( {\mathfrak{o}}^{\star}(4) \) symmetries
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Publication:1706997
DOI10.1007/JHEP11(2017)187zbMath1383.83027arXiv1708.09848WikidataQ62579616 ScholiaQ62579616MaRDI QIDQ1706997
Andrzej Zdzisław Borowiec, Jerzy Lukierski, Valeriy N. Tolstoy
Publication date: 28 March 2018
Published in: Journal of High Energy Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1708.09848
Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Quantization of the gravitational field (83C45) Noncommutative geometry in quantum theory (81R60) Quaternion and other division algebras: arithmetic, zeta functions (11R52)
Related Items (8)
Basic quantizations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \( {\mathfrak{o}}^{\star}(4) \) symmetries ⋮ The q-linked complex Minkowski space, its real forms and deformed isometry groups ⋮ Quantum twist-deformed \(D = 4\) phase spaces with spin sector and Hopf algebroid structures ⋮ \(\kappa\)-deformed BMS symmetry ⋮ Quantum d = 3 Euclidean and Poincaré symmetries from contraction limits ⋮ Quantum Klein space and superspace ⋮ 3-dimensional \(\Lambda\)-BMS symmetry and its deformations ⋮ Interpolations between Jordanian twists induced by coboundary twists
Cites Work
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- Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
- A Jordanian deformation of AdS space in type IIB supergravity
- Yang-Baxter sigma models based on the CYBE
- Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
- A \((2+1)\) non-commutative Drinfel'd double spacetime with cosmological constant
- \(2+1\)-dimensional gravity as an exactly soluble system
- What is a classical r-matrix?
- Noncommutative spacetimes. Symmetries in noncommutative geometry and field theory
- Quantum deformations of \(D =4\) Lorentz algebra revisited: Twistings of \(q\) -deformation
- Jordanian twist quantization of \(D=4\) Lorentz and Poincaré algebras and \(D=3\) contraction limit
- Generalised Chern-Simons actions for 3d gravity and \(\kappa \)-Poincaré symmetry
- Compact matrix pseudogroups
- New quantum deformation of \(SL(2,\mathbb{C}{})\). Hopf algebra level
- On a non-standard algebraic description of integrable nonlinear systems
- Poisson structures on the Lorentz group
- Poisson structures on Poincaré group
- Yang-Baxter sigma models and Lax pairs arising from \(\kappa\)-Poincaré \(r\)-matrices
- Basic quantizations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \( {\mathfrak{o}}^{\star}(4) \) symmetries
- Observables and dispersion relations in \(\kappa\)-Minkowski spacetime
- \(N=\frac 12\) deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras
- Algebraic aspects of integrable systems: in memory of Irene Dorfman
- Symplectic structure of the moduli space of flat connection on a Riemann surface
- The quantum structure of spacetime of the Planck scale and quantum fields
- Quantization of Lie bialgebras. I
- \(\kappa \)-deformations and extended \(\kappa \)-Minkowski spacetimes
- Quantum deformations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \(\mathfrak{o}^\star(4)\) symmetries in unified \(\mathfrak{o}(4; \mathbb{C})\) setting
- Quantization of semi-classical twists and noncommutative geometry
- Semi-classical twists for \(\mathfrak{sl}_3\) and \(\mathfrak{sl}_4\) boundary \(r\)-matrices of Cremmer-Gervais type
- On classical Yang-Baxter based deformations of the \(\mathrm{ADS}_5\times \mathrm{S}^5\) superstring
- Drinfel'd doubles for (2+1)-gravity
- Braided tensor products and the covariance of quantum noncommutative free fields
- BRAIDED FIELD QUANTIZATION FROM QUANTUM POINCARÉ COVARIANCE
- On integrability of the Yang–Baxter σ-model
- Twisted Quantum Deformations of Lorentz and Poincar\'{e} algebras
- Quantum symmetry, the cosmological constant and Planck-scale phenomenology
- NEW CLASS OF QUANTUM DEFORMATIONS OF D = 4 EUCLIDEAN SUPERSYMMETRIES
- Deformed integrableσ-models, classicalR-matrices and classical exchange algebra on Drinfel’d doubles
- Hopf algebras for physics at the Planck scale
- The quantum Heisenberg group H(1)q
- Real and imaginary forms of quantum groups
- On some unsolved problems in quantum group theory
- Hamiltonian theory over noncommutative rings and integrability in multidimensions
- QUANTIZATION ENFORCES INTERACTION: QUANTUM MECHANICS OF TWO PARTICLES ON A QUANTUM SPHERE
- On quantum Lie algebras and quantum root systems
- Poisson-Lie structures on Poincaré and Euclidean groups in three dimensions
- Background independent quantum gravity: a status report
- Covariant realization of quantum spaces as star products by Drinfeld twists
- Klein and conformal superspaces, split algebras and spinor orbits
- Maximally extended $\boldsymbol {\mathfrak{sl}(2\vert 2)}$ , q-deformed $\boldsymbol{\mathfrak{d}{(2, 1;\epsilon)}}$ and 3D kappa-Poincaré
- Modern Canonical Quantum General Relativity
- BASIC TWIST QUANTIZATION OF osp(1|2) AND κ-DEFORMATION OF D = 1 SUPERCONFORMAL MECHANICS
- A Grassmann and graded approach to coboundary Lie bialgebras, their classification, and Yang-Baxter equations
- Solutions of the classical Yang-Baxter equation for simple Lie algebras
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