Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra

In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, gauge-invariant model has been presented by gauging algebra. We firstly construct Stelle–West-like action for five-dimensional spacetime in which effects spontaneous symmetry breaking have taken into account. doing so, we get an extended version Einstein’s field equations. Next, decompose Lie establish MacDowell–Mansouri-like that contains Einstein–Hilbert term, cosmological term as well new terms coming from four-dimensional where torsion-free condition assumed. Finally, shown both models are equivalent appropriately chosen gauge condition.