
TL;DR
This paper introduces rooted tree maps derived from Hopf algebra of rooted trees, which generate relations among multiple zeta values, advancing understanding in algebraic structures related to number theory.
Contribution
It constructs a new class of linear maps on noncommutative polynomial algebra based on rooted trees and proves their role in relating multiple zeta values.
Findings
Rooted tree maps induce new relations among multiple zeta values.
The construction is based on Hopf algebra of rooted trees by Connes and Kreimer.
The maps provide a novel algebraic framework for studying multiple zeta values.
Abstract
Based on Hopf algebra of rooted trees introduced by Connes and Kreimer, we construct a class of linear maps on noncommutative polynomial algebra in two indeterminates, namely rooted tree maps. We also prove that their maps induce a class of relations among multiple zeta values.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Graph theory and applications
