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

在本文中，构建了（反）de Sitter 代数的半简单和麦克斯韦扩展。然后，通过测量（反）德西特代数的麦克斯韦半简单扩展，提出了规范不变模型。我们首先为五维时空构建了一个类 Stelle-West 模型动作，其中考虑了自发对称破坏的影响。通过这样做，我们得到了爱因斯坦场方程的扩展版本。接下来，我们分解五维扩展李代数并建立一个 MacDowell-Mansouri-like 作用，其中包含爱因斯坦-希尔伯特项、宇宙学项以及来自四维时空麦克斯韦扩展的新项，其中无扭假设条件。最后，