On split involutive regular BiHom-Lie superalgebras
On split involutive regular BiHom-Lie superalgebras
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DOI：
10.1515/math-2020-0144
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发表时间：
2020-01
期刊：
影响因子：
1.7
通讯作者：
Shuangjian Guo;Xiaohui Zhang;Shengxiang Wang
中科院分区：
文献类型：
--
作者：
Shuangjian Guo;Xiaohui Zhang;Shengxiang Wang
摘要 本文的目的是研究分裂对合正则 BiHom-Lie 超代数的结构，它可以看作是分裂对合正则 Hom-Lie 代数和分裂正则 BiHom-Lie 超代数的自然推广。通过开发此类代数的根连接技术，我们证明了这种分裂的对合正则 BiHom-Lie 超代数 L {\mathfrak{L}} 的形式为 L = U + Σ α I α {\mathfrak{L}}=U+{\sum }_{\alpha }{I}_{\alpha }，其中 U 是最大阿贝尔子代数 H 的子空间和任意 I α ，一个明确描述的理想 L {\mathfrak{L}} ，如果 [α] ≠ [β]，则满足 [I α , I β ] = 0。在 L {\mathfrak{L}} 具有最大长度的情况下，L {\mathfrak{L}} 的简单性也体现在根的连接方面。
Abstract The goal of this paper is to examine the structure of split involutive regular BiHom-Lie superalgebras, which can be viewed as the natural generalization of split involutive regular Hom-Lie algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split involutive regular BiHom-Lie superalgebra L {\mathfrak{L}} is of the form L = U + ∑ α I α {\mathfrak{L}}=U+{\sum }_{\alpha }{I}_{\alpha } with U a subspace of a maximal abelian subalgebra H and any I α , a well-described ideal of L {\mathfrak{L}} , satisfying [I α , I β ] = 0 if [α] ≠ [β]. In the case of L {\mathfrak{L}} being of maximal length, the simplicity of L {\mathfrak{L}} is also characterized in terms of connections of roots.