Abstract

We discuss a q deformation of the formalism proposed by Stelle and West and Grignani and Nardelli using the quantum Poincaré algebra. It is shown that the q-deformed formalism permits constructing an action for (3+1)-dimensional q gravity genuinely invariant under ISO(3,1). It is proved that, in the context of a q-Poincaré gauge formulation, q gravity in 3+1 dimensions can be dimensionally reduced to gravity in 2+1 dimensions with or without a cosmological constant. The dimensional reduction is consistent with the gauge symmetries, mapping ISOq(3,1) gauge transformations onto ISOq(2,1) ones. © 2002 The American Physical Society.