Left counital Hopf algebras on free Nijenhuis algebras
Xing Gao, Peng Lei, Tianjie Zhang
TL;DR
This paper constructs a left counital Hopf algebra structure on free Nijenhuis algebras by establishing a unique factorization, defining a coproduct, and proving connectedness, advancing algebraic theory.
Contribution
It introduces a novel left counital Hopf algebra structure on free Nijenhuis algebras based on unique factorization and bialgebraic construction.
Findings
Established unique factorization in free Nijenhuis algebras
Defined a coproduct and left counital bialgebraic structure
Proved the bialgebra is connected, leading to a Hopf algebra
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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