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In order to study the structure of arbitrary split Leibniz triple systems, we introduce the class of split Leibniz triple systems as the natural extension of the class of split Lie triple systems and split Leibniz algebras. By developing techniques of connections of roots for this kind of triple systems, we show that any of such Leibniz triple systems $T$ with a symmetric root system is of the form $T=U+\sum_{[j]\in \Lambda^{1}/\sim} I_{[j]}$ with $U$ a subspace of $T_{0}$ and any $I_{[j]}$ a well described ideal of $T$, satisfying $\{I_{[j]},T,I_{[k]}\} =\{I_{[j]},I_{[k]},T\}=\{T,I_{[j]},I_{[k]}\}=0$ if $[j]\neq [k]$.
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참고문헌 (15)
참고문헌 신청
S. Albeverio / 2005 / On nilpotent and simple Leibniz algebras / Comm. Algebra 33(1):159~172
S. Albeverio / 2006 / Cartan subalgebras, weight spaces, and criterion of solvability of finite dimen-sional Leibniz algebras / Rev. Mat. Complut 19(1):183~195
S. Ayupov / 1998 / On Leibniz algebras, Algebra and operator theory / Kluwer Acad. Publ :1~12
D. W. Barnes / 2012 / On Engel’s theorem for Leibniz algebras / Comm. Algebra 40(4):1388~1389
D. W. Barnes / 2012 / On Levi’s theorem for Leibniz algebras / Bull. Aust. Math. Soc 86(2):184~185
S. Albeverio / 2006 / Cartan subalgebras, weight spaces, and criterion of solvability of finite dimen-sional Leibniz algebras / Rev. Mat. Complut 19(1):183~195
S. Ayupov / 1998 / On Leibniz algebras, Algebra and operator theory / Kluwer Acad. Publ :1~12
D. W. Barnes / 2012 / On Engel’s theorem for Leibniz algebras / Comm. Algebra 40(4):1388~1389
D. W. Barnes / 2012 / On Levi’s theorem for Leibniz algebras / Bull. Aust. Math. Soc 86(2):184~185
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