145 citations · 646 across the 26 of their papers we have counts for
8 papers · 1 filter
A Symplectic Representation of
Tevian Dray, Corinne A. Manogue, Robert A. Wilson
We explicitly construct a particular real form of the Lie algebra in terms of symplectic matrices over the octonions, thus justifying the identifications $\mathfra…
Octonionic Cayley Spinors and E6
Tevian Dray, Corinne A. Manogue
Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptio…
Octonions, E6, and Particle Physics
Corinne A. Manogue, Tevian Dray
In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this conditio…
Orthonormal Eigenbases over the Octonions
Tevian Dray, Corinne A Manogue, Susumu Okubo
We previously showed that the real eigenvalues of 3x3 octonionic Hermitian matrices form two separate families, each containing 3 eigenvalues, and each leading to an orthonormal de…
Some Properties of 3x3 Octonionic Hermitian Matrices with Non-Real Eigenvalues
Tevian Dray, Jason Janesky, Corinne A. Manogue
We discuss our preliminary attempts to extend previous work on 2x2 Hermitian octonionic matrices with non-real eigenvalues to the 3x3 case.
Octonionic Hermitian Matrices with Non-Real Eigenvalues
Tevian Dray, Jason Janesky, Corinne A. Manogue
We extend previous work on the eigenvalue problem for Hermitian octonionic matrices by discussing the case where the eigenvalues are not real, giving a complete treatment of the 2x…