论文标题
薄弱的代数
Weak stuffle algebras
论文作者
论文摘要
由Q-shuffle产品由歌手Q-Analogues确定的Q-Shuffle产品的启发，我们在本文中构建了以薄弱的混音和材料产品的概括和弹药产品的概括。然后，我们表征了弱的洗牌产品，并举例说明了两个或三个基数字母的情况。我们专注于在经典情况下和弱情况下尊重的代数结构之间的比较。与经典情况一样，每个弱的洗牌产物都可以配备树突状结构。但是，它们对四方代数和HOPF代数结构具有另一种行为。我们给出了一些弱小产品满足的关系。
Motivated by q-shuffle products determined by Singer from q-analogues of multiple zeta values, we build in this article a generalisation of the shuffle and stuffle products in terms of weak shuffle and stuffle products. Then, we characterise weak shuffle products and give as examples the case of an alphabet of cardinality two or three. We focus on a comparison between algebraic structures respected in the classical case and in the weak case. As in the classical case, each weak shuffle product can be equipped with a dendriform structure. However, they have another behaviour towards the quadri-algebra and the Hopf algebra structure. We give some relations satisfied by weak stuffle products.
