我们阐明了基于简单的形式实Jordan代数的矩阵模型的几何。这样的约当代数产生了一种非结合几何，它是洛伦兹几何的推广。本文重点讨论了例外Jordan代数和例外Jordan C ~*-代数的构造，并描述了与例外立方矩阵模型和E_6矩阵模型有关的射影空间。由此产生的投影空间被证明是例外版本的投影扭量空间，从而揭示了存在例外扭量弦论是对偶的八元矩阵模型。
英文摘要：
We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry. We emphasize constructions for the exceptional Jordan algebra and the exceptional Jordan C*-algebra and describe the projective spaces related to the exceptional cubic matrix model and the E_6 matrix model. The resulting projective spaces are shown to be exceptional versions of projective twistor space, thus revealing the existence of exceptional twistor string theories that are dual to octonionic matrix models.
Scalar-tensor theories in the Lyra geometry: Invariance under local transformations of length units and the Jordan-Einstein frame conundrum
Centro Brasileiro de Pesquisas Fı́sicas (CBPF)（巴西中心物理研究）；Universidade Federal do Espı́rito Santo (UFES)（圣埃斯皮里图联邦大学）；Universidade do Estado do Rio de Janeiro (UERJ)（里约热内卢州立大学）
