from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. A relationship between three vector spaces.
from the GNU version of the Collaborative International Dictionary of English
- n. Three united; state of being three.
from The Century Dictionary and Cyclopedia
- n. A union or junction of three; threeness: a word invented after the model of duality.
Sorry, no etymologies found.
There are three 8 dimensional representations-the vector, spinor and conjugate spinor, related by a symmetry called triality that can be seen to underlie the structure of the supersymmetry algebras between 8 and 11 dimensions.
There are three E_8's there which under a triality define as well an 8 + 3 = 11 dimensional space, which under this condition is compactified to 10.
The number three plays a most interesting role with the triality in group theories, such as the 3 + bar-3 long roots of SU (3) which have some connection to the three families of quarks.
Here we can see the second and third generations of matter now related to the first generation by a symmetry called "triality."
This is a triality structure, and what this exceptional group does is to put the Grassmannian (Fermionic) fields on the same frame bundle with the gauge fields.
But in Agni is found the first triality, which, philosophically, is interpreted as a trinity.
In comparing the Açvins to other pairs  this dual nature is frequently referred to; but no less is there a triality in connection with them which often in describing them has been ignored.
Eygar 15: 36, 1 November 2007 (EDT) (a) it's not Latin, it's Greek. (b) in the Greek idiom, there is not a duality of polar opposites, it is a triality, philia, phobia, and phagia -- attraction, repulsion, and consumption.
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