Triality — Tri*al i*ty, n. [L. tres, tria, three.] Three united; state of being three. [R.] H. Wharton. [1913 Webster] … The Collaborative International Dictionary of English
triality — trīality / alˈi ti/ noun • • • Main Entry: ↑trial … Useful english dictionary
Triality — In mathematics, triality is a relationship between three vector spaces, analogous to the duality relation between dual vector spaces. Most commonly, it describes those special features of the group Spin(8), the double cover of 8 dimensional… … Wikipedia
triality — noun A relationship between three vector spaces … Wiktionary
SO(8) — In mathematics, SO(8) is the special orthogonal group acting on eight dimensional Euclidean space. It could be either a real or complex simple Lie group of rank 4 and dimension 28. Like all special orthogonal groups (except SO(2)), SO(8) is not… … Wikipedia
Octonion — In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold . There are only four such algebras, the other three being the real numbers R, the … Wikipedia
Spin structure — In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical … Wikipedia
An Exceptionally Simple Theory of Everything — is a preprint proposing a basis for a unified field theory, named E8 Theory , which attempts to describe all known fundamental interactions in physics, and to stand as a possible theory of everything. The preprint was posted to the physics arXiv… … Wikipedia
Dynkin diagram — See also: Coxeter–Dynkin diagram Finite Dynkin diagrams Affine (extended) Dynkin diagrams … Wikipedia
Spinor — In mathematics and physics, in particular in the theory of the orthogonal groups (such as the rotation or the Lorentz groups), spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the… … Wikipedia
