Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras

Abstract

We consider a superextension of the extended Jordanian twist, describing nonstandard quantization of anti-de-Sitter ($AdS$) superalgebra $osp(1|4)$ in the form of Hopf superalgebra. The super-Jordanian twisting function and corresponding basic coproduct formulae for the generators of $osp(1|4)$ are given in explicit form. The nonlinear transformation of the classical superalgebra basis not modifying the defining algebraic relations but simplifying coproducts and antipodes is proposed. Our physical application is to interpret the new super-Jordanian deformation of $osp(1|4)$ superalgebra as deformed D=4 $AdS$ supersymmetries. Subsequently we perform suitable contraction of quantum Jordanian $AdS$ superalgebra and obtain new $\kappa$-deformation of D=4 Poincare superalgebra, with the bosonic sector describing the light cone $\kappa$-deformation of Poincare symmetries.

arXiv commentLaTeX,13 pages, comments and references added, to be published in Eur.Phys.J.C

References in corpus (28)

• String Theory and Noncommutative Geometry
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Non-commutative superspace from string theory
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory
• Non(anti)commutative Superspace
• Deformed Field Theory on kappa-spacetime
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• Braided Momentum Structure of the q-Poincare Group
• Some Aspects of Deformations of Supersymmetric Field Theories
• Extended jordanian twists for Lie algebras
• Gauge theories on the kappa-Minkowski spacetime
• On the classification of quantum Poincaré groups
• A New Null-Plane Quantum Poincare Algebra
• Dirac spinors for Doubly Special Relativity and $\kappa$-Minkowski noncommutative spacetime
• κ-deformations of D=4 Weyl and conformal symmetries
• Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters
• Field theory on kappa-spacetime
• Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1 Superconformal Mechanics
• Twist Deformation of the rank one Lie Superalgebra
• Peripheric Extended Twists
• The Kappa-Weyl group and its algebra
• Non-standard quantum so(3,2) and its contractions
• Super-Jordanian Quantum Superalgebra ${\mathcal{U}}_h(osp(2/1))$
• $\kappa$-Deformation of Poincaré Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure
• $\kappa$-deformations of D=3 conformal versus deformations of D=4 AdS symmetries
• Deformation of orthosymplectic Lie superalgebra osp(1|2)

Cited by in corpus (20)

• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Kappa-deformed Snyder spacetime
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• Jordanian Twist Quantization of D=4 Lorentz and Poincare Algebras and D=3 Contraction Limit
• N=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• Twisted submanifolds of R^n
• New twisted quantum deformations of D=4 super-Poincare algebra
• Multiparameter Quantum Deformations of Jordanian Type for Lie Superalgebras
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• On super-Jordanian ${\mathcal{U}}_{\mathsf{h}}(sl(N|1))$ algebra
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime