结合超代数上的交叉同态
Crossed Homomorphisms on associative superalgebras
浏览论文内容
中文总结 AI 辅助
本文引入结合超代数上交叉同态的概念，通过刻画其与关联分次李代数Maurer–Cartan元素的对应关系构建其上同调理论，研究形式形变并明确无穷小部分与延拓障碍的上同调性质。
中文摘要 AI 辅助
本文引入结合超代数上交叉同态的概念，证明交叉同态恰好是自然关联的分次李代数的Maurer–Cartan元素。该刻画使我们能构建交叉同态的上同调理论，进而研究其形式形变并推导对应形变方程。已证明，形式形变的无穷小部分是关联上同调中的1-上闭链，而有限阶形变延拓的障碍是2-上闭链。
英文摘要
In this paper, we introduce the notion of crossed homomorphisms on associative superalgebras. We show that crossed homomorphisms are precisely the Maurer--Cartan elements of a naturally associated graded Lie algebra. This characterization enables us to construct a cohomology theory of crossed homomorphisms. We then investigate formal deformations of crossed homomorphisms and derive the corresponding deformation equations. It is proved that the infinitesimal part of a formal deformation is a 1-cocycle in the associated cohomology, while the obstruction to extending a deformation of finite order is a 2-cocycle.
