Jacobi algebras and Jacobi Novikov-Poisson algebras
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910021035491328 |
|---|---|
| author | Lu, Chengyang Hong, Yanyong |
| author_facet | Lu, Chengyang Hong, Yanyong |
| contents | In this paper, we introduce the notion of Jacobi Novikov-Poisson algebras and demonstrate that their affinization yields Jacobi algebras. We note that every unital differential Novikov-Poisson algebra is also a Jacobi Novikov-Poisson algebra. Additionally, any Jacobi Novikov-Poisson algebra gives rise to a Jacobi algebra, either by taking the commutator bracket of its underlying Novikov algebra or by using a derivation. We provide classifications of low-dimensional Jacobi Novikov-Poisson algebras including those of dimensions 2 and 3 over $\mathbb{C}$ up to isomorphism and show that the tensor product of two such algebras remains a Jacobi Novikov-Poisson algebra. Several further constructions of Jacobi Novikov-Poisson algebras from existing ones are also presented. The notion of Frobenius Jacobi Novikov-Poisson algebras is introduced, and several equivalent characterizations are established in terms of quadratic structures and integrals. Classifications of quadratic Jacobi Novikov-Poisson algebras of dimensions 2 and 3 over $\mathbb{C}$ are given. Finally, we provide an explicit construction of Frobenius Jacobi algebras using finite-dimensional quadratic Jacobi Novikov-Poisson algebras and finite-dimensional quadratic right Jacobi Novikov-Poisson algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12516 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Jacobi algebras and Jacobi Novikov-Poisson algebras Lu, Chengyang Hong, Yanyong Rings and Algebras In this paper, we introduce the notion of Jacobi Novikov-Poisson algebras and demonstrate that their affinization yields Jacobi algebras. We note that every unital differential Novikov-Poisson algebra is also a Jacobi Novikov-Poisson algebra. Additionally, any Jacobi Novikov-Poisson algebra gives rise to a Jacobi algebra, either by taking the commutator bracket of its underlying Novikov algebra or by using a derivation. We provide classifications of low-dimensional Jacobi Novikov-Poisson algebras including those of dimensions 2 and 3 over $\mathbb{C}$ up to isomorphism and show that the tensor product of two such algebras remains a Jacobi Novikov-Poisson algebra. Several further constructions of Jacobi Novikov-Poisson algebras from existing ones are also presented. The notion of Frobenius Jacobi Novikov-Poisson algebras is introduced, and several equivalent characterizations are established in terms of quadratic structures and integrals. Classifications of quadratic Jacobi Novikov-Poisson algebras of dimensions 2 and 3 over $\mathbb{C}$ are given. Finally, we provide an explicit construction of Frobenius Jacobi algebras using finite-dimensional quadratic Jacobi Novikov-Poisson algebras and finite-dimensional quadratic right Jacobi Novikov-Poisson algebras. |
| title | Jacobi algebras and Jacobi Novikov-Poisson algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2602.12516 |