Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1 Superconformal Mechanics

Abstract

The twisting function describing a nonstandard (super-Jordanian) quantum deformation of $osp(1|2)$ is given in explicite closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed $osp(1|2)$ superalgebras are considered. One real quantum $osp(1|2)$ superalgebra is interpreted as describing the $\kappa$-deformation of D=1, N=1 superconformal algebra, which can be applied as a symmetry algebra of N=1 superconformal mechanics.

13 pages,LaTeX, v2. References added, typos corrected

References in corpus (9)

• Black Holes and Superconformal Mechanics
• Extended jordanian twists for Lie algebras
• Superconformal mechanics, black holes, and non-linear realizations
• The Geometry of (Super) Conformal Quantum Mechanics
• Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters
• On Integrable Models Related to the $osp(1,2)$ Gaudin Algebra
• Creation operators and Bethe vectors of the osp(1|2) Gaudin model
• Twist Deformation of the rank one Lie Superalgebra
• New Quantum Deformation of Osp(1;2)

Cited by in corpus (16)

• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• Once again about quantum deformations of D=4 Lorentz algebra: twistings of q-deformation
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Quantizations of D=3 Lorentz symmetry
• Twist Deformations of the Supersymmetric Quantum Mechanics
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• Deformation of orthosymplectic Lie superalgebra osp(1|2)
• Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials
• On super-Jordanian ${\mathcal{U}}_{\mathsf{h}}(sl(N|1))$ algebra