Abstract
We consider the curvatures 2-form associated with AdSL4-valued one-form gauge connection, and then we construct a four-dimensional action that generalize the Einstein-Hilbert gravity. It is shown that the Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use of the Inönü-Wigner contraction method. In the same way, by gauging the AdSL5-spacetime algebra, the Einstein-Hilbert gravity is extended including the vector fields kμab and hμa which are associated with non-Abelian tensors and non Abelian vectors charges in the AdSL5 algebra.The B5 extension of Einstein gravity can be obtained from AdSL5-gravity using of the above mentioned contraction procedure. Some aspects of a gravity based on the algebra AdSL6 are considered in an appendix.
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