Isomorphism between Hopf algebras for multiple zeta values
Number Theory
2026-03-09 v2 Quantum Algebra
Abstract
The classical quasi-shuffle algebra for multiple zeta values have a well-known Hopf algebra structure. Recently, the shuffle algebra for multiple zeta values are also equipped with a Hopf algebra structure. This paper shows that these two Hopf algebras are isomorphic utilizing quasi-symmetric functions. This Hopf algebra isomorphism is compared with with the well-known isomorphism between the shuffle Hopf algebra and quasi-shuffle Hopf algebra of Hoffman, Newman and Radford.
Cite
@article{arxiv.2512.24732,
title = {Isomorphism between Hopf algebras for multiple zeta values},
author = {Li Guo and Hongyu Xiang and Bin Zhang},
journal= {arXiv preprint arXiv:2512.24732},
year = {2026}
}
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