1999/06/09 by Jamil Daboul, J Daboul, R Delbourgo +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebra over a field #Algebraic and Geometric Analysis #Mathematics and Applications #Matrix (chemical analysis) #Matrix multiplication #Matrix representation #Multiplication (music) #Real representation #Representation (politics) #hep-th
paper · pdf · doi:10.1063/1.532950
published as J.Math.Phys. 40 (1999) 4134-4150 · 18 printed pages
arxiv created 1999/06/09 · openalex publication_date 1999/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We define a special matrix multiplication among a special subset of 2N×2N matrices, and study the resulting (nonassociative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative nonassociative, and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers; they naturally lead to the Cayley–Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac’s equation for a free particle. A few other results and remarks arise as byproducts.