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:
“Their martyred blood and ashes sow
O’er all the Italian fields where still doth sway
The triple tyrant; that from these may grow
A hundredfold, who, having learnt thy way,
Early may fly the Babylonian woe.”
—John Milton (1608–1674)
“Short of a wholesale reform of college athletics—a complete breakdown of the whole system that is now focused on money and power—the women’s programs are just as doomed as the men’s are to move further and further away from the academic mission of their colleges.... We have to decide if that’s the kind of success for women’s sports that we want.”
—Christine H. B. Grant, U.S. university athletic director. As quoted in the Chronicle of Higher Education, p. A42 (May 12, 1993)