A brief review of the essentials behind the construction of a Chern-Simons-like brane action from the Large N limit of Exceptional Jordan Matrix Models paves the way to the construction of actions for membranes and p-branes moving in octonionic-spacetime backgrounds endowed with octonionic-valued metrics. It is found that the action of a membrane moving in spacetime backgrounds endowed with an octonionic-valued metric is not invariant under the usual diffeomorphisms of its world volume coordinates ${\sigma }^a\to {\sigma }^{\prime a}({\sigma }^b)$, but instead, it is invariant under the rigid $E_{6(-26)}$ transformations which preserve the volume (cubic) form. An extensive study of the bosonic octonionic string moving in flat backgrounds, and its quantization, follows. One of the most significant findings (without invoking supersymmetry) is that the number of degrees of freedom of three (massless) fermion generations is the same as the number of transverse dimensions of an octonionic string moving in $D=26$ octonionic dimensions. The star-product deformations of octonionic p-branes follow. In particular, we focus on the octonionic membrane along with the phase space quantization methods developed by [30] within the context of Nonassociative Quantum Mechanics. We finalize with an analysis of two octonionic gravitational actions and with some concluding remarks on Double and Exceptional Field theories, Nonassociative Gravity and $A_{\infty },L_{\infty }$ algebras.

简要回顾一下从异常乔丹矩阵模型的大N极限构造类似Chern-Simons的麸皮动作背后的要点，这为在质子-时空背景下运动的膜和p-大脑动作的构造铺平了道路。辛酸值度量。研究发现，在时空背景下，具有辛酸值的量度的膜的运动在其世界体积坐标的通常变态作用下不是不变的。${\sigma }^{\mathrm{一种}}\to {\sigma }^{\prime \mathrm{一种}}（{\sigma }^b）$，但是在刚性条件下它是不变的 $E_{6（-26）}$保留体积（立方）形式的转换。接下来是对在平坦背景下移动的玻音正弦弦及其量化的广泛研究。最重要的发现之一（不引起超对称）是三个（无质量）费米子世代的自由度数与在其中移动的八维音弦的横向尺寸数相同。$d=26$渗透压尺寸。随之而来的是调子对p形星的星型变形。尤其是，我们将重点放在八元膜上，以及由[30]在非缔合量子力学的背景下开发的相空间量化方法。最后，我们分析了两个重张引力作用，并对双场和超场理论，非缔合引力理论和非引力场理论作了一些总结性说明。${\mathrm{一种}}_{\infty }，{\mathrm{大号}}_{\infty }$ 代数