Left counital Hopf algebras on free Nijenhuis algebras |
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| Authors: | Xing Gao Peng Lei |
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| Affiliation: | School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu, P. R. China |
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| 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. |
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| Keywords: | Bracketed words factorization left counital bialgebra left counital Hopf algebra Nijenhuis algebra |
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