| Presented by Tevian Dray, professor of mathematics and Corinne Manogue, professor of physics; both of Oregon State University. Drs. Dray and Manogue will present each Wednesday, beginning Sept. 16, for 3-5 weeks.
The octonions are a generalization of the familiar real and complex numbers. However, the octonions are neither commutative (ab not equal to ba) nor associative [a (bc) not equal to (ab)]. Linear algebra over the octonions is therefore both fun and interesting! Remarkably, this algebra appears to be closely related both to deep mathematics, such as the exceptional Lie groups, and to deep physics, such as the existence of supersymmetry and string theory.
We will begin by explaining some of the mathematical properties of octonions, and then discuss some applications to physics. We envision a series of three to five 1-hour sessions; a tentative outline appears below:
I. Basic Properties, eigenvalue problems
II. Symmetry groups (rotations, Lorentz group, exceptional groups)
III. The Dirac equation: leptons
IV. The Cayley plane: E6 and quarks |
