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We consider the extension of the general-linear and special-linear algebrasby employing the Maxwell symmetry in $D$ space-time dimensions. We show howvarious Maxwell extensions of the ordinary space-time algebras can be obtainedby a suitable contraction of generalized algebras. The extended Lie algebrascould be useful in the construction of generalized gravity theories and theobjects that couple to them. We also consider the gravitational dynamics ofthese algebras in the framework of the gauge theories of gravity. By adoptingthe symmetry-breaking mechanism of the Stelle-West model, we present somemodified gravity models that contain the generalized cosmological constant termin four dimensions.

Gauging the Maxwell extended $\mathcal{GL}\left(n,\mathbb{R}\right)$ and $\mathcal{SL}\left(n+1,\mathbb{R}\right)$ algebras