Algebraic aspects of rooted tree maps
Algebraic aspects of rooted tree maps
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有根树图的代数方面
DOI：
10.1007/s11139-022-00612-1
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Tanaka Tatsushi
中科院分区：
文献类型：
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作者：
Murahara Hideki;Tanaka Tatsushi
在根树的Connes-Kreimer Hopf代数的基础上，将根树映射定义为非交换多项式代数上的线性映射.众所周知，它们诱导了一大类多个zeta值的线性关系。本文证明了对任意根树f，存在唯一的多项式，它能显式地给出根树映射的象。我们还将对极映射刻画为特殊映射的共轭。
Based on the Connes–Kreimer Hopf algebra of rooted trees, rooted tree maps are defined as linear maps on the noncommutative polynomial algebra. It is known that they induce a large class of linear relations for multiple zeta values. In this paper, we show for any rooted treefthere exists a unique polynomial inthat gives the image of the rooted tree mapexplicitly. We also characterize the antipode maps as the conjugation by the special map.