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Lie Triple Systems | Open Access Journals
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Journal of Applied & Computational Mathematics

ISSN: 2168-9679

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Lie Triple Systems

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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