Left counital Hopf algebras on free Nijenhuis algebras. (English) Zbl 1400.16023
Summary: 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.
MSC:
| 16T10 | Bialgebras |
| 16U30 | Divisibility, noncommutative UFDs |
| 08B20 | Free algebras |
| 16T05 | Hopf algebras and their applications |
| 16T30 | Connections of Hopf algebras with combinatorics |
Keywords:
bracketed words; factorization; left counital bialgebra; left counital Hopf algebra; Nijenhuis algebraReferences:
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