## 69 Citations

### Nonassociative differential geometry and gravity with non-geometric fluxes

- MathematicsJournal of High Energy Physics
- 2018

We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to…

### Quantum-Corrected Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type

- Mathematics, Physics
- 2017

A general formula for the curvature of a central metric, w.r.t a noncommutative spacetime of general Lie-algebraic type is calculated by using the generalized braiding formalism. Furthermore, we…

### Noncommutative solitons of gravity

- Physics, Mathematics
- 2009

We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only. We found various kinds of nontrivial solutions by applying a similar…

### Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

- Mathematics
- 2009

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel’d twists. We…

### Non-commutative Einstein equations and Seiberg-Witten map

- Mathematics
- 2011

The Seiberg--Witten map is a powerful tool in non-commutative field theory, and it has been recently obtained in the literature for gravity itself, to first order in non-commutativity. This paper,…

### Riemannian curvature of the noncommutative 3-sphere

- Mathematics
- 2015

In order to investigate to what extent the calculus of classical (pseudo-)Riemannian manifolds can be extended to a noncommutative setting, we introduce pseudo-Riemannian calculi of modules over…

### A noncommutative catenoid

- MathematicsLetters in mathematical physics
- 2018

It is proved that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated.

### Noncommutative Supergravity

- Physics
- 2011

We present a noncommutative extension of ﬁrst order Einstein-Hilbert gravity in the context of twist-deformed space-time, with a ? -product associated to a triangular Drinfeld twist. In particular…

## References

SHOWING 1-10 OF 39 REFERENCES

### Star product geometries

- Mathematics
- 2009

We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows us to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of…

### Noncommutative geometry and gravity

- Mathematics
- 2006

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…

### Noncommutative Symmetries and Gravity

- Mathematics
- 2006

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

### Noncommutative gravity in two dimensions

- Mathematics
- 2002

We deform a two-dimensional topological gravity making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that…

### Noncommutative D=4 gravity coupled to fermions

- Mathematics
- 2009

We present a noncommutative extension of Einstein-Hilbert gravity in the context of twist-deformed space-time, with a -product associated to a quite general triangular Drinfeld twist. In particular…

### Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory

- Mathematics, Physics
- 2009

Deformed Field Theory: Physical Aspects.- Differential Calculus and Gauge Transformations on a Deformed Space.- Deformed Gauge Theories.- Einstein Gravity on Deformed Spaces.- Deformed Gauge Theory:…

### Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes

- Mathematics, Physics
- 2009

As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations…

### Elements of Noncommutative Geometry

- Mathematics
- 2000

This volume covers a wide range of topics including sources of noncommutative geometry; fundamentals of noncommutative topology; K-theory and Morita equivalance; noncommutative integrodifferential…