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Lie ternary system

From Encyclopedia of Mathematics
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A vector space with a trilinear composition

satisfying the following conditions:

If is a Lie algebra and is a subspace such that for any , then the operation

converts into a Lie ternary system. Conversely, every Lie ternary system can be obtained in this way from some Lie algebra.

The category of finite-dimensional Lie ternary systems over the field is equivalent to the category of simply-connected symmetric homogeneous spaces (see Symmetric space).

References

[1] S. Helgason, "Differential geometry, Lie groups, and symmetric spaces" , Acad. Press (1978)
[2] O. Loos, "Symmetric spaces" , 1 , Benjamin (1969)
How to Cite This Entry:
Lie ternary system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lie_ternary_system&oldid=18380
This article was adapted from an original article by A.S. Fedenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article