发表机构
Henan Normal University（河南师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过交叉积数据分析n-李代数非阿贝尔扩张的导子与自同构，利用上同调类分类扩张数据，构造相关李代数与群并得到Wells序列，还处理了稀疏交叉积相关内容。
AI 中文摘要
我们通过完全交叉积数据研究任意非阿贝尔n-李代数扩张的导子与自同构。其相对中心是一个典范系数模，存在一个三阶上同调类阻碍满足混合Filippov恒等式的数据的完备化；当该类消失时，相对二阶上同调空间对剩余的扩张数据进行分类。我们证明了一个非阿贝尔良准则，构造了相容对的李代数与群，得到带有显式提升方程的导子与自同构Wells序列。导子阻碍是李代数1-上闭链，加法自同构阻碍是交叉同态。我们区分了普通中心与相对中心、核的外导子与所需的混合作用，还处理了稀疏交叉积，包括其二阶混合运算的表示类及控制稀疏截面变化的附加方程。
英文摘要
We study derivations and automorphisms of arbitrary non-abelian extensions of $n$-Lie algebras through their full crossed-product data. Their relative center is a canonical coefficient module, and a third cohomology class obstructs completion of data satisfying the mixed Filippov identities. When this class vanishes, a relative second cohomology space classifies the remaining extension data. We prove a non-abelian good criterion, construct the Lie algebra and group of compatible pairs, and obtain derivation and automorphism Wells sequences with explicit lifting equations. The derivation obstruction is a Lie algebra $1$-cocycle; the additive automorphism obstruction is a crossed homomorphism. We distinguish the ordinary center from the relative center, and outer derivations of the kernel from the mixed action required. Sparse crossed products are treated, including the representation class of their second mixed operation and the additional equations governing changes of sparse sections.
Comments49 pages, 0 figures,continue of arXiv:2609.05051
