2009/10/09 by Jonathan M. Evans, Evans, Jonathan M.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Finite Group Theory Research #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.0910.1828
openalex publication_date 2009/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.