One-parameter deformations of the diassociative and dendriform operads
One-parameter deformations of the diassociative and dendriform operads
复制标题
DOI：
10.1080/03081087.2016.1183563
复制
发表时间：
2016-02
影响因子：
1.1
通讯作者：
M. Bremner
中科院分区：
文献类型：
--
作者：
M. Bremner
Livernet和Loday构造了一个具有一个运算的非对称结合运算的极化为一个具有两个运算（李括号和Jordan积）的对称运算，并定义了一个包含Poisson代数的单参数变形。我们结合联合收割机这与树状分裂的结合操作到两个nonassociative操作的总和，并使用Koszul对偶二次运算，构造单参数变形的非对称树状和双结合运算到对称运算的范畴。
Livernet and Loday constructed a polarization of the nonsymmetric associative operad with one operation into a symmetric operad with two operations (the Lie bracket and Jordan product), and defined a one-parameter deformation of , which includes Poisson algebras. We combine this with the dendriform splitting of an associative operation into the sum of two nonassociative operations, and use Koszul duality for quadratic operads, to construct one-parameter deformations of the nonsymmetric dendriform and diassociative operads into the category of symmetric operads.