Communications in Number Theory and Physics
Volume 13 (2019)
Rooted tree maps
Pages: 647 – 666
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.
Hopf algebra of rooted trees, noncommutative polynomial algebra, multiple zeta values, quasi-derivation relation, Kawashima’s relation
2010 Mathematics Subject Classification
05C05, 05C25, 11M32, 16T05
The author is grateful to scientific members and staffs in Max-Planck-Institut für Mathematik for their hospitality, where this work has been done. He is also thankful to Dr. Henrik Bachmann for helpful comments and advice. This work is also supported by Kyoto Sangyo University Research Grants.
Received 21 April 2018
Accepted 5 July 2019
Published 8 August 2022