1993/06/02 by Frank Dodd Tony Smith, F. D. T. Smith, Smith, F. D. T.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Graph theory and applications #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9306011
1+22 pages, THEP-93-5, LaTex
arxiv created 1993/06/02 · openalex publication_date 1993/06/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The relation between Geisteswissenschaft and Naturwissenschaft has been discussed by Munster in hep-th/9305104. The plan of this paper is to begin with the empty set; use it to form sets and quivers (sets of points plus sets of arrows between pairs of points); and then use them to make complex vector spaces and to get the A-D-E Coxeter-Dynkin diagrams. The Dn Spin(2n) Lie algebras have spinor representations to describe fermions. D4 Spin(8) triality gives automorphisms among its vector and two half-spinor representations. D5 Spin(10) contains both Spin(8) and the complexification of the vector representation of Spin(8). E6 contains both Spin(10) and the two half-spinor representations of Spin(10), and therefore contains the adjoint representation of Spin(8) and the complexifications of the vector and the two half-spinor representations of Spin(8). E6 is the basis for construction of a fundamental model of physics that is consistent with experiment (see hep-th/9302030, hep-ph/9301210).