On the algebra of quasi-shuffles
On the algebra of quasi-shuffles
复制标题
DOI：
10.1007/s00229-007-0086-2
复制
发表时间：
2005-06
影响因子：
0.6
通讯作者：
J. Loday
中科院分区：
文献类型：
--
作者：
J. Loday
对于任意交换代数，张量模上的洗牌积(R)可以变形为一个新积。它被称为拟洗牌代数或填充代数，记作tq (R)。我们证明了在多项式代数中，对于一些称为交换三元代数（CTD-algebras）的代数结构，entq (R)是自由的。这一结果是ctd -双代数的结构定理的一部分，它是作为协代数结合的，其本原部分是交换的。换句话说，有一个类似于（Com,As,Lie）的操作数三元组（As，CTD,Com）。在最后一部分中，我们给出了非交换条件下拟洗牌代数的类似解释。
For any commutative algebraRthe shuffle product on the tensor moduleT(R) can be deformed to a new product. It is called the quasi-shuffle algebra, or stuffle algebra, and denotedTq(R). We show that ifRis the polynomial algebra, thenTq(R) is free for some algebraic structure called Commutative TriDendriform (CTD-algebras). This result is part of a structure theorem for CTD-bialgebras which are associative as coalgebras and whose primitive part is commutative. In other words, there is a good triple of operads (As,CTD,Com) analogous to (Com,As,Lie). In the last part we give a similar interpretation of the quasi-shuffle algebra in the noncommutative setting.