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Left counital Hopf algebras on free Nijenhuis algebras

Xing Gao, Peng Lei, Tianjie Zhang
2018 Communications in Algebra  

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2018 pre-print arXiv:1805.07693v1 fatcat:223o4olvzjcvdo4pd5ryrincby
Factorization in algebra is an important problem. In this paper, we first obtain a unique factorization in free Nijenhuis algebras. By using of this unique factorization, we then define a coproduct and a left counital bialgebraic structure on a free Nijenhuis algebra. Finally, we prove that this left counital bialgebra is connected and hence obtain a left counital Hopf algebra on a free Nijenhuis algebra.
doi:10.1080/00927872.2018.1459641 fatcat:4cmg24qbojehjjsb5oakcesyqa
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Xing Gao, Peng Lei, Tianjie Zhang. "Left counital Hopf algebras on free Nijenhuis algebras." Communications in Algebra 46.11 (2018) 4868-4883