Einstein-Riemann Gravity on Deformed Spaces
Julius Wess
TL;DR
This paper develops a noncommutative version of Einstein-Riemann gravity using star product formalism, deforming the algebra of diffeomorphisms and the associated Hopf algebra to explore gravity on noncommutative spaces.
Contribution
It introduces a framework for formulating Einstein-Riemann gravity on noncommutative spaces by deforming the underlying algebraic structures.
Findings
Deformation of the Hopf algebra of diffeomorphisms
Construction of differential calculus on noncommutative spaces
Formulation of gravity theory in the star product formalism
Abstract
A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the deformed gravity is based on a deformation of the Hopf algebra.
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