In algebra, a triple system is a vector space V over a field F together with a F-trilinear map
The most important examples are Lie triple systems and Jordan triple systems. They were introduced by Nathan Jacobson in 1949 to study subspaces of associative algebras closed under triple commutators, w] and triple anticommutators {u, {v, w}}. In particular, any Lie algebra defines a Lie triple system and any Jordan algebra defines a Jordan triple system. They are important in the theories of symmetric spaces, particularly Hermitian symmetric spaces and their generalizations (symmetric R-spaces and their noncompact duals).
Read more about Triple System: Lie Triple Systems, Jordan Triple Systems, Jordan Pair, See Also
Famous quotes containing the words triple and/or system:
“The triple pillar of the world transformed
Into a strumpet’s fool.”
—William Shakespeare (1564–1616)
“The twentieth-century artist who uses symbols is alienated because the system of symbols is a private one. After you have dealt with the symbols you are still private, you are still lonely, because you are not sure anyone will understand it except yourself. The ransom of privacy is that you are alone.”
—Louise Bourgeois (b. 1911)