Jordan Pairs | Open Access Journals

Journal of Applied & Computational Mathematics

ISSN: 2168-9679

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Jordan Pairs

Lie triple systems, and Jordan triple systems are the most important examples. In 1949 Nathan Jacobson introduced them to study subspaces of associative algebras closed under triple switches [[u, v], w] and triple anticommutators {u,{v, w}}. Specifically any Lie algebra defines a triple Lie system. Any Algebra in Jordan describes a triple scheme in Jordan. They are important in symmetric space theories, particularly Hermitian symmetric spaces and their generalizations (symmetric R-spaces and noncompact duals).

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