论文标题
$ f [x] $上的重量为零的射击式rota-baxter操作员
Injective Rota-Baxter operators of weight zero on $F[x]$
论文作者
论文摘要
Rota-baxter操作员对整体操作员的零件公式进行了积分的自然概括。 2015年，郑，郭和罗森克兰兹（Rosenkranz）猜想，在多项式代数$ \ mathbb {r} [x] $上，每个注射式rota rota-baxter ota ota-baxter运算符都是乘以非零多项式和正式集成的乘法的组成。我们在任何特征零字段上确认了这种猜想。此外，我们在这些运算符的模量空间上建立了一个索引的结构，并描述了一般模态二的加性结构。最后，我们对编成一个子集提供无限的传递作用。
Rota-Baxter operators present a natural generalisation of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota-Baxter operator of weight zero on the polynomial algebra $\mathbb{R}[x]$ is a composition of the multiplication by a nonzero polynomial and a formal integration at some point. We confirm this conjecture over any field of characteristic zero. Moreover, we establish a structure of an ind-variety on the moduli space of these operators and describe an additive structure of generic modality two on it. Finally, we provide an infinitely transitive action on codimension one subsets.
