Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces

Abstract

We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four dimensional space.

arXiv comment18 pages

References in corpus (30)

• The Spectral Action Principle
• Algebras of distributions suitable for phase-space quantum mechanics. I
• Quantum group gauge theory on quantum spaces
• Moyal Planes are Spectral Triples
• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Infinitely many star products to play with
• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Noncommutative epsilon-graded connections
• Quantum gauge theories on noncommutative 3-d space
• Laplace-Runge-Lenz vector in quantum mechanics in noncommutative space
• Gauge theories of quantum groups
• Noncommutative $R^d$ via closed star product
• A generalization of the Jordan-Schwinger map: classical version and its q--deformation
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Submanifolds and Quotient Manifolds in Noncommutative Geometry
• On the $\star$-product quantization and the Duflo map in three dimensions
• Noncommutative differential calculus for Moyal subalgebras
• Matrix Bases for Star Products: a Review
• Gauged Laplacians on quantum Hopf bundles
• Lie algebra type noncommutative phase spaces are Hopf algebroids
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Calculi, Hodge operators and Laplacians on a quantum Hopf fibration
• Examples of derivation-based differential calculi related to noncommutative gauge theories
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• (A class of) Hodge duality operators over the quantum SU(2)
• Warped Products and Yang-Mills equations on non commutative spaces
• A Hodge - De Rham Dirac operator on the quantum $\mathrm{SU}(2)$

Cited by in corpus (6)

• A novel approach to non-commutative gauge theory
• Symmetries and Reduction -- part I -- Poisson and symplectic picture
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• A Simple Model of Double Dynamics on Lie Groups
• Abstract Dynamical Systems: Remarks on Symmetries and Reduction
• Quantum Calculi: differential forms and vector fields in noncommutative geometry