论文标题
单一作业和代数的同源物
Homologies of monomial operads and algebras
论文作者
论文摘要
我们考虑单一非阴谋相关代数的栏络合物$ a = k \ langle x \ rangle /（w_1，...，...，w_t）$。它将其分为直接的复合物$ b_w $，定义为任何固定的单元$ W = x_1 ... x_n \ a $中的x_n \。 我们提出了一个简单的论点，表明该子复合的同源性最多是一维的，并描述了出现非平凡同源性的位置。就$ w \在$中的$ w \中相关的广义堤防路径的长度而言，它具有非常简单的表达。 考虑了有关同源性二分法问题的经营类似物。结果表明，二分法是在单一树木关系形成秩序的情况下保持的。给出了例子，表明一般的二分法和同源纯度不存在。对于二次作战，开发了用于计算同源性关系图的组合工具。给出了使用这些方法计算截短的二进制作业中同源性的示例。
We consider the bar complex of a monomial non-unital associative algebra $A=k \langle X \rangle / (w_1,...,w_t)$. It splits as a direct sum of complexes $B_w$, defined for any fixed monomial $w=x_1...x_n \in A$. We give a simple argument, showing that the homology of this subcomplex is at most one-dimensional, and describe the place where the nontrivial homology appears. It has a very simple expression in terms of the length of the generalized Dyck path associated to a given monomial in $w \in A$. The operadic analogue of the question about dichotomy in homology is considered. It is shown that dichotomy holds in case when monomial tree-relations form an order. Examples are given showing that in general dichotomy and homological purity does not hold. For quadratic operads, the combinatorial tool for calculating homology in terms of relation graphs is developed. Example of using these methods to compute homology in truncated binary operads is given.
