A Hopf algebra on (0,1)-matrices

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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Publication Details

Journal
Mathematical Modelling and Control
Published
2025-01-01
DOI
https://doi.org/10.3934/mmc.2025014
Primary Topic
Advanced Topics in Algebra
Type
article
Field-Weighted Citation Impact
0.00
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article

A Hopf algebra on (0,1)-matrices

Huilan Li, Sifan Song
Mathematical Modelling and Control
Advanced Topics in Algebra
article

A Hopf algebra on (0,1)-matrices

Huilan Li, Sifan Song
article en

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.

Mathematical Modelling and ControlVol. 5(2)
Shandong Normal University (CN)
Openalex Percentile: Top 83%
Advanced Topics in Algebra
DOIOpen Access PDFOpenAlex
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A Hopf algebra on (0,1)-matrices — Huilan Li, Sifan Song · Mathematical Modelling and Control (2025) | TGRS Research Map | TGRS