Nijenhuis algebras, NS algebras, and N-dendriform algebras. (English) Zbl 1262.16040
A Nijenhuis algebra is a nonunitary associative algebra \(N\) with a linear endomorphism \(P\) satisfying \(P(x)P(y)=P(P(x)y)+P(xP(y))-P^2(xy)\) for all \(x,y\in N\).
The paper under review studies relationship between associative Nijenhuis algebras and NS algebras. The paper starts with a construction of a free Nijenhuis algebra over an algebra which is then applied to construct the universal enveloping Nijenhuis algebra of an NS algebra. At the end of the paper the authors determine the N-dendriform algebra compatible with the Nijenhuis algebra.
The paper under review studies relationship between associative Nijenhuis algebras and NS algebras. The paper starts with a construction of a free Nijenhuis algebra over an algebra which is then applied to construct the universal enveloping Nijenhuis algebra of an NS algebra. At the end of the paper the authors determine the N-dendriform algebra compatible with the Nijenhuis algebra.
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
| 16W10 | Rings with involution; Lie, Jordan and other nonassociative structures |
| 17A30 | Nonassociative algebras satisfying other identities |
| 16S10 | Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) |
| 16S30 | Universal enveloping algebras of Lie algebras |
| 16T25 | Yang-Baxter equations |
Keywords:
free Nijenhuis algebras; NS algebras; dendriform algebras; Rota-Baxter algebras; categories; universal enveloping Nijenhuis algebrasReferences:
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