Noncommutative Gravity and the *-Lie algebra of diffeomorphisms

@article{Aschieri2007NoncommutativeGA,
  title={Noncommutative Gravity and the *-Lie algebra of diffeomorphisms},
  author={Paolo Aschieri},
  journal={Protein Science},
  year={2007}
}
  • P. Aschieri
  • Published 2 March 2007
  • Physics
  • Protein Science
We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincaré) Lie algebra allows to construct a noncomutative theory of gravity. PACS: 02.40.Gh, 02.20.Uw, 04.20.-q, 11.10.Nx, 04.60.-m. 2000 MSC: 83C65, 53D55, 81R60, 58B32 This article is based on common work with Christian Blohmann, Marija Dimitrijević, Frank Meyer, Peter Schupp, Julius Wess [1, 2] and on [3… 

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References

SHOWING 1-10 OF 19 REFERENCES

A gravity theory on noncommutative spaces

A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter θ. The algebraic relations remain the same, whereas the

Noncommutative Symmetries and Gravity

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into

AN INTRODUCTION TO NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON QUANTUM GROUPS

We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q→1 limit). The Lie derivative and the contraction

Noncommutative geometry and gravity

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of

Bicovariant quantum algebras and quantum Lie algebras

AbstractA bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun $$(\mathfrak{G}_q )$$ toUqg, given by elements of the pure

Differential calculus on compact matrix pseudogroups (quantum groups)

The paper deals with non-commutative differential geometry. The general theory of differential calculus on quantum groups is developed. Bicovariant bimodules as objects analogous to tensor bundles

Gravity and the structure of noncommutative algebras

A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation