试探与例外李代数：DECONSTRUCTING幻方
Trialities and Exceptional Lie Algebras: DECONSTRUCTING the Magic Square
摘要：
一个建设的幻方，因此例外李代数，进行使用trialities而不是司代数。通过准备，一个全面的讨论trialities给出，纳入一些新的结果和证明。许多技术都与理论物理中常见的思想密切相关，或源于这些思想。阐明了对称空间在幻方构造中的重要性，允许以统一和透明的方式验证每个代数的Jacobi性质，而不需要详细的计算。对应于其他对称空间的一个变化的建设，也给出了。
英文摘要：
A construction of the magic square, and hence of exceptional Lie algebras, is carried out using trialities rather than division algebras. By way of preparation, a comprehensive discussion of trialities is given, incorporating a number of novel results and proofs. Many of the techniques are closely related to, or derived from, ideas which are commonplace in theoretical physics. The importance of symmetric spaces in the magic square construction is clarified, allowing the Jacobi property to be verified for each algebra in a uniform and transparent way, with no detailed calculations required. A variation on the construction, corresponding to other symmetric spaces, is also given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
