Lattices generated by discrete Jordan algebras

Journal Article · Thu Sep 01 04:00:00 EDT 1988 · Mod. Phys. Letters B; (United States)

DOI:https://doi.org/10.1142/S0217732388001380· OSTI ID:6206305

Gursey, F

The discrete Jordan Algebras of 1 x 1, 2 x 2, and 3 x 3 hermitiain matrices over integer elements of the four division algebras are considered. They are transformed under discrete subgroups of groups associated with the magic square. Points corresponding to a discrete Jordan matrix belong to a lattice generated by Weyl reflections that are expressed by means of Jacobson's triple product. Special cases include the O(32), E/sub 8/ x E/sub 8/ and E/sub 10/ lattices that occur in superstring theories.

• Research Organization: Center for Theoretical Physics, Sloane Lab., Yale Univ., New Haven, CT (US)
• OSTI ID: 6206305
• Journal Information: Mod. Phys. Letters B; (United States), Journal Name: Mod. Phys. Letters B; (United States) Vol. 3:12; ISSN MPLBE
• Country of Publication: United States
• Language: English

Related Subjects

645300 -- High Energy Physics-- Particle Invariance Principles & Symmetries
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASIA
COMPOSITE MODELS
DEVELOPING COUNTRIES
EXTENDED PARTICLE MODEL
FIELD ALGEBRA
FIELD THEORIES
FUNCTIONS
HERMITIAN MATRIX
JACOBIAN FUNCTION
JORDAN
LATTICE FIELD THEORY
MATHEMATICAL MODELS
MATRICES
PARTICLE MODELS
QUANTUM FIELD THEORY
QUARK MODEL
STRING MODELS
SUPERSYMMETRY
SYMMETRY