Left counital Hopf algebras on free Nijenhuis algebras

ABSTRACT

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.

KEYWORDS:

• Bracketed words
• factorization
• left counital bialgebra
• left counital Hopf algebra
• Nijenhuis algebra

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W99
• 08B20
• 16T10
• 16T05
• 16T30

Acknowledgments

We thank the anonymous referee for valuable suggestions helping to improve the paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11501466), Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2017-162), and the Natural Science Foundation of Gansu Province (Grant No. 17JR5 RA175) and Shandong Province (No. ZR2016AM02).