Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space

Abstract

Extending a recently proposed procedure of construction of various elements of diffential geometry on noncommutative algebras, we obtain these structures on noncommutative superalgebras. As an example, a quantum superspace covariant under the action of super-Jordanian $OS{p}_h(2/1)$ is studied. It is shown that there exist a two paramater family of torsionless connections, and the curvature computed from this family of connections is bilinear. It is also shown that the connections are not compatible with the metric.

19 pages

References in corpus (18)

• Quantum Field Theory on Noncommutative Spaces
• Gravity in Non-Commutative Geometry
• Connections on central bimodules
• Linear Connections in Non-Commutative Geometry
• On Curvature in Noncommutative Geometry
• Linear connections on the quantum plane
• On the first order operators in bimodules
• Linear connections on matrix geometries
• Differential Calculus on the Quantum Superspace and Deformation of Phase Space
• h-deformation of GL(1|1)
• Noncommutative Geometry of the h-deformed Quantum Plane
• Classification of Low Dimensional Lie Super-Bialgebras
• Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1 Superconformal Mechanics
• Twist Deformation of the rank one Lie Superalgebra
• Linear Connections on the Two Parameter Quantum Plane
• Super-jordanian deformation of the orthosymplectic Lie superalgebras
• Super-Jordanian Quantum Superalgebra ${\mathcal{U}}_h(osp(2/1))$
• New Quantum Deformation of Osp(1;2)

Cited by in corpus (5)

• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Bicovariant differential calculus on the superspace ${\mathbb{R}}_q(1|2)$
• Quantum Spheres for OSp_q(1/2)
• Covariant Differential Calculi on $S{P}_q^{1|2}$
• Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials