The Lagrangian of q-Poincare' Gravity

Abstract

The gauging of the q-Poincaré algebra of ref. hep-th 9312179 yields a non-commutative generalization of the Einstein-Cartan lagrangian. We prove its invariance under local q-Lorentz rotations and, up to a total derivative, under q-diffeomorphisms. The variations of the fields are given by their q-Lie derivative, in analogy with the q=1 case. The algebra of q-Lie derivatives is shown to close with field dependent structure functions. The equations of motion are found, generalizing the Einstein equations and the zero-torsion condition.

12 pp., LaTeX, DFTT-01/94 (extra blank lines introduced by mailer, corrupting LaTeX syntax, have been hopefully eliminated)

References in corpus (5)

• An introduction to non-commutative differential geometry on quantum groups
• Differential Geometry on Linear Quantum Groups
• Gauge theories of quantum groups
• Cartan Calculus for Hopf Algebras and Quantum Groups
• Quantum Groups, Non-Commutative Differential Geometry and Applications

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