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.

中文翻译：

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关于分裂对合正则 BiHom-Lie 超代数

摘要 本文的目的是考察分裂对合正则BiHom-Lie超代数的结构，它可以看作分裂对合正则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对合正则 BiHom-Lie 超代数 L {\mathfrak{L}} 的形式为 L = U + ∑ α I α {\mathfrak{L }}=U+{\sum }_{\alpha {I}_{\alpha } 其中 U 是最大阿贝尔子代数 H 和任意 I α 的子空间，是 L {\mathfrak{L}} 的一个很好描述的理想, 满足 [I α , I β ] = 0 如果 [α] ≠ [β]。在 L {\mathfrak{L}} 是最大长度的情况下，L {\mathfrak{L}} 的简单性也以根的连接为特征。