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| NON-DEGENERATE INVARIANT BILINEAR FORMS ON NONASSOCIATIVE TRIPLE SYSTEMS |
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Citation： |
ZHAO Lina,LI Xuewen,ZHANG Zhixue.NON-DEGENERATE INVARIANT BILINEAR FORMS ON NONASSOCIATIVE TRIPLE SYSTEMS[J].Chinese Annals of Mathematics B,2005,26(2):275~290 |
| Page view： 1395
Net amount： 842 |
Authors： |
ZHAO Lina; LI Xuewen;ZHANG Zhixue |
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| Abstract： |
A bilinear form f on a nonassociative triple system T is said to be invariant if
and only if f( abc , d) = f(a, dcb ) = f(c, bad ) for all a, b, c, d ∈ T . (T , f) is called
a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition
theory for triple systems and pseudo-metric triple systems is established. Moreover, the
finite-dimensional metric Lie triple systems are characterized in terms of the structure
of the non-degenerate, invariant and symmetric bilinear forms on them. |
Keywords： |
Triple system, Lie triple system, Bilinear form, Lie algebra |
Classification： |
17A40 |
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