Noncommutative Symmetries and Gravity

preprint2006arXivOpen access

Abstract

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.

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