Irreducible Lie–Yamaguti algebras
Irreducible Lie–Yamaguti algebras
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DOI：
10.1016/j.jpaa.2008.09.003
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发表时间：
2008-10
影响因子：
0.8
通讯作者：
Pilar Benito;A. Elduque;Fabi'an Mart'in-Herce
中科院分区：
文献类型：
--
作者：
Pilar Benito;A. Elduque;Fabi'an Mart'in-Herce
Lie-Yamaguti代数（或广义李三系）是与约化齐性空间密切相关的二元-三元代数。不可约为李内导子代数上模的李-Yamaguti代数是各向同性不可约齐性空间的代数对应。这些系统将被分成三个不相交的类型：伴随类型，非简单类型和泛型类型。前两种类型的系统将被分类，其中大部分将被证明是与李代数的广义山雀结构有关。
Lie–Yamaguti algebras (or generalized Lie triple systems) are binary–ternary algebras intimately related to reductive homogeneous spaces. The Lie–Yamaguti algebras which are irreducible as modules over their Lie inner derivation algebra are the algebraic counterpart of the isotropy irreducible homogeneous spaces. These systems will be shown to split into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types will be classified and most of them will be shown to be related to a Generalized Tits Construction of Lie algebras.