Structure Theorems of Mixable Shuffle Algebras
Structure Theorems of Mixable Shuffle Algebras
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DOI：
10.1080/00927872.2012.663430
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发表时间：
2013-05
影响因子：
0.7
通讯作者：
Li Guo;Bingyong Xie
中科院分区：
文献类型：
--
作者：
Li Guo;Bingyong Xie
混合洗牌代数是众所周知的洗牌代数和拟洗牌代数的推广，具有广泛的应用。本文在Radford关于有理系数的洗牌代数是Lyndon词中的多项式代数的著名工作的推动下，研究了带系数的可混合洗牌代数的环理论结构。为了考虑正特征p域中的系数，我们仔细研究了林登词及其p变分。因此，我们通过提供显式的生成器和关系集，确定了一类相当大的可混合洗牌代数的结构。
Mixable shuffle algebras are generalizations of the well-known shuffle algebra and quasi-shuffle algebra with broad applications. In this article we study the ring theoretic structures of mixable shuffle algebras with coefficients in a field motivated by the well-known work of Radford that a shuffle algebra with rational coefficients is a polynomial algebra in Lyndon words. To consider coefficients in a field of positive characteristic p, we carefully study the Lyndon words and their p-variations. As a result, we determine the structures of a quite large class of mixable shuffle algebras by providing explicit sets of generators and relations.