n-李代数的扩张结构
Extending Structures for $n$-Lie Algebras
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中文总结 AI 辅助
本文从三个角度重新研究n-李代数的上同调理论，重点探讨其扩张结构，得到统一乘积判据及相关特例，还研究了分解、形变映射等问题。
中文摘要 AI 辅助
我们从三个不同角度重新研究n-李代数的上同调理论：莱布尼茨代数的上同调理论、无穷小形变与阿贝尔扩张。本文主要部分研究n-李代数的扩张结构，得到了一个充要的统一乘积判据，并将交叉积、稀疏非阿贝尔扩张、匹配对等情形作为特例进行研究。我们还探讨了n-李代数的分解、形变映射与补问题，附录部分移除了具有所有中间混合分量的一般非约化统一乘积。
英文摘要
Motivated by the Casas-Loday-Pirashvili maps concerning representations of $n$-Leibniz algebras, we give an intrinsic characterization of the cohomology of $n$-Lie algebras with coefficient in a representation space $V$. We investigated the cohomology theory of $n$-Lie algebras in three different ways: cohomology theory of Leibniz algebras, infinitesimal deformation and abelian extension. In the main part of this paper, we solve the extending problems for $n$-Lie algebras. A necessary and sufficient unified-product criterion is obtained. The case of crossed products, sparse non-abelian extensions, matched pairs are studied as special cases. We also investigate the factorizations, deformation maps, and complements problem for $n$-Lie algebras. An appendix removes the general non-reduced unified product with all intermediate mixed components.
发表机构
- Henan Normal University（河南师范大学）
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