论文标题
婴儿珠的表示
Baby bead representations
论文作者
论文摘要
本文是由Turchin和Willwacher的珠子表示的研究所激发的。这里的问题是根据自由谎言代数的Lie代数同源性重新制定的，该代数在伴随代表的张量产品中具有系数。 主要思想是利用杀死长度大于两个的谎言支架给出的系数的截断。尽管这种截断是残酷的，但它保留了明确的结果，保留了重要的，高度的不平凡的信息。 使用将问题分为两个步骤，将“同源性”计算与“反对称化”分开。这涉及一些辅助类别，包括对上围墙的Brauer类别的概括。 这种方法通过标题的“婴儿珠表示”，为此获得了完整的结果。作为一种应用，针对新的无限家族计算了Turchin和Willwacher珠子表示的组成因子。
This paper is motivated by the study of Turchin and Willwacher's bead representations. The problem is reformulated here in terms of the Lie algebra homology of a free Lie algebra with coefficients in tensor products of the adjoint representation. The main idea is to exploit the truncation of the coefficients given by killing Lie brackets of length greater than two. Although this truncation is brutal, it retains significant and highly non-trivial information, as exhibited by explicit results. A dévissage is used that splits the problem into two steps, separating out a `homology' calculation from `antisymmetrization'. This involves some auxiliary categories, including a generalization of the upper walled Brauer category. This approach passes through the `baby bead representations' of the title, for which complete results are obtained. As an application, the composition factors of Turchin and Willwacher's bead representations are calculated for a new infinite family.
