A Hopf algebra on (0,1)-matrices

Sifan Song; Huilan Li; Sifan Song; Huilan Li

doi:10.3934/mmc.2025014

Mathematical Modelling and Control

2025, Volume 5, Issue 2: 193-201. doi: 10.3934/mmc.2025014

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Research article

A Hopf algebra on (0,1)-matrices

Sifan Song ,
Huilan Li ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Received: 27 February 2023 Revised: 08 October 2023 Accepted: 19 November 2023 Published: 29 May 2025

In this paper, we defined that a conjunction multiplication and an unshuffle comultiplication on the vector space spanned by (0,1)-matrices. Then, we proved that the vector space with these two operations is a bialgebra. In fact, it is a graded connected bialgebra, so it is a Hopf algebra.
- Hopf algebra,
- (0,1)-matrix,
- conjunction multiplication,
- unshuffle comultiplication
Citation: Sifan Song, Huilan Li. A Hopf algebra on (0,1)-matrices[J]. Mathematical Modelling and Control, 2025, 5(2): 193-201. doi: 10.3934/mmc.2025014

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Abstract

In this paper, we defined that a conjunction multiplication and an unshuffle comultiplication on the vector space spanned by (0,1)-matrices. Then, we proved that the vector space with these two operations is a bialgebra. In fact, it is a graded connected bialgebra, so it is a Hopf algebra.

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