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arXiv · 2512.24732

Isomorphism between Hopf algebras for multiple zeta values

Li Guo·Hongyu Xiang·Bin Zhang
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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.

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Li Guo, Hongyu Xiang, Bin Zhang. 2025-12-31. Isomorphism between Hopf algebras for multiple zeta values. https://arxiv.org/abs/2512.24732

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