Noncommutative Gravity and the *-Lie algebra of diffeomorphisms

Abstract

We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincare) Lie algebra allows to construct a noncomutative theory of gravity.

12 pages. Presented at the Erice International School of Subnuclear Physics, 44th course, Erice, Sicily, 29.8- 7.9 2006, and at the Second workshop and midterm meeting of the MCRTN ``Constituents, Fundamental Forces and Symmetries of the Universe" Napoli, 9-13.10 2006

References in corpus (6)

• String Theory and Noncommutative Geometry
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Noncommutative Geometry and Gravity
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• Noncommutative Symmetries and Gravity

Cited by in corpus (9)

• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Twisted Covariant Noncommutative Self-dual Gravity
• Field Theory on Nonanticommutative Superspace
• Noncommutative gravity with self-dual variables
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Thermofield dynamics and Gravity
• On Non-Commutative Correction of the Gödel-type Metric
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field