\(RB\)-operator and Nijenhuis operator on Hom-associative conformal algebra. (English) Zbl 07916050
Summary: Hom-associative conformal algebra \(\mathcal{A}\) is an associative conformal algebra with a twist map and satisfies the Hom-associative conformal identity. This study aims to introduce the notion of the Rota-Baxter operator \(\mathcal{R}\) on Hom-associative conformal algebra \(\mathcal{A}\). We generalize our study to Hom-dendriform and Hom-tridendriform conformal algebras and give their relation to Hom-preLie conformal algebras. We give the interrelation between dendriform (and tridendriform) algebra with Hom-associative conformal Rota-Baxter algebra. Furthermore, we explore the Nijenhus operator on Hom-associative conformal algebra and describe its relation with Hom-associative Rota-Baxter operator.
MSC:
| 17A30 | Nonassociative algebras satisfying other identities |
| 15A99 | Basic linear algebra |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 16G30 | Representations of orders, lattices, algebras over commutative rings |
Keywords:
conformal algebra; Hom-associative conformal algebra; Hom-associative Rota-Baxter conformal algebra; Hom-dendriform conformal algebra; Nijenhuis conformal algebra; Hom-preLie conformal algebraReferences:
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