论文标题
树突形代数相对于半群
Dendriform Algebras Relative to a Semigroup
论文作者
论文摘要
在过去的二十年中，Loday的Dendriform代数及其兄弟姐妹在lie和Zinbiel的兄弟姐妹中受到了关注。在最近的文献中，人们对这些类型的代数的概括引起了兴趣，其中每个单独的操作都被固定的半群$ s $索引的运营家族所取代。该注释的目的是双重的。首先，我们通过证明对最熟悉的代数类型已经可能出现类似的扩展名来添加现有工作：交换性，联想性和谎言。其次，我们表明这些概念从分类的角度自然而然地以统一的方式出现。为此，只需考虑代数的标准类型，而是参考$ s $ raded的矢量空间的单体类别。
Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual operation is replaced by a family of operations indexed by a fixed semigroup $S$. The purpose of this note is twofold. First, we add to the existing work by showing that a similar extension is possible already for the most familiar types of algebra: commutative, associative, and Lie. Second, we show that these concepts arise naturally and in a unified manner from a categorical perspective. For this, one simply has to consider the standard types of algebra but in reference to the monoidal category of $S$-graded vector spaces.
