有限维Cartan型模李超代数的保积Hom-结构

华秀英, 唐黎明, 刘文德

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 365-372.

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PDF(435 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 365-372. DOI: 10.12386/A2015sxxb0037
论文

有限维Cartan型模李超代数的保积Hom-结构

    华秀英1, 唐黎明2, 刘文德2
作者信息 +

Multiplicative Hom-Structures on Finite Dimensional Modular Lie Superalgebras of Cartan Type

    Xiu Ying HUA1, Li Ming TANG2, Wen De LIU2
Author information +
文章历史 +

摘要

在特征大于 3 的代数闭域上,利用 Cartan型模李超代数的自然滤过不变性,通过计算 Cartan 型模李超代数的 Hom-映射在其 -1分支上的作用,本文证明了有限维 Cartan 型模李超代数的保积Hom-结构是平凡的.

Abstract

Let F be an algebraically closed field of characteristic p > 3. Using the invariance of the natural filtration and calculating the actions on the -1 components for the Hom-structures of the modular Lie superalgebras under consideration, we prove that there exists only the trivial multiplicative Hom-structures on the finite dimensional Z-graded modular Lie superalgebras of Cartan type.

关键词

李超代数 / Hom-结构 / 滤过

Key words

Lie superalgebras / Hom-structure / filtration

引用本文

导出引用
华秀英, 唐黎明, 刘文德. 有限维Cartan型模李超代数的保积Hom-结构. 数学学报, 2015, 58(3): 365-372 https://doi.org/10.12386/A2015sxxb0037
Xiu Ying HUA, Li Ming TANG, Wen De LIU. Multiplicative Hom-Structures on Finite Dimensional Modular Lie Superalgebras of Cartan Type. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 365-372 https://doi.org/10.12386/A2015sxxb0037

参考文献

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基金

国家自然科学基金(11171055, 11471090);黑龙江省教育厅科学技术研究项目(12521114, 12541246);哈尔滨理工大学青年科学研究基金(2011YF006)

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