Infinite-dimensional pre-Lie bialgebras via affinization of pre-Novikov bialgebras
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911030499606528 |
|---|---|
| author | Li, Yue Hong, Yanyong |
| author_facet | Li, Yue Hong, Yanyong |
| contents | In this paper, we show that there is a pre-Lie algebra structure on the tensor product of a pre-Novikov algebra and a right Novikov dialgebra and the tensor product of a pre-Novikov algebra and a special right Novikov algebra on the vector space of Laurent polynomials being a pre-Lie algebra characterizes the pre-Novikov algebra. The latter is called the affinization of a pre-Novikov algebra. Moreover, we extend this construction of pre-Lie algebras and the affinization of pre-Novikov algebras to the context of bialgebras. We show that there is a completed pre-Lie bialgebra structure on the tensor product of a pre-Novikov bialgebra and a quadratic Z-graded right Novikov algebra. Moreover, a pre-Novikov bialgebra can be characterized by the fact that its affinization by a quadratic Z-graded right Novikov algebra on the vector space of Laurent polynomials gives an infinite-dimensional completed pre-Lie bialgebras. Note that the reason why we choose a quadratic right Novikov algebra instead of a right Novikov dialgebra with a special bilinear form is also given. Furthermore, we construct symmetric completed solutions of the S-equation in the induced pre-Lie algebra by symmetric solutions of the pre-Novikov Yang-Baxter equation in a pre-Novikov algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite-dimensional pre-Lie bialgebras via affinization of pre-Novikov bialgebras Li, Yue Hong, Yanyong Rings and Algebras In this paper, we show that there is a pre-Lie algebra structure on the tensor product of a pre-Novikov algebra and a right Novikov dialgebra and the tensor product of a pre-Novikov algebra and a special right Novikov algebra on the vector space of Laurent polynomials being a pre-Lie algebra characterizes the pre-Novikov algebra. The latter is called the affinization of a pre-Novikov algebra. Moreover, we extend this construction of pre-Lie algebras and the affinization of pre-Novikov algebras to the context of bialgebras. We show that there is a completed pre-Lie bialgebra structure on the tensor product of a pre-Novikov bialgebra and a quadratic Z-graded right Novikov algebra. Moreover, a pre-Novikov bialgebra can be characterized by the fact that its affinization by a quadratic Z-graded right Novikov algebra on the vector space of Laurent polynomials gives an infinite-dimensional completed pre-Lie bialgebras. Note that the reason why we choose a quadratic right Novikov algebra instead of a right Novikov dialgebra with a special bilinear form is also given. Furthermore, we construct symmetric completed solutions of the S-equation in the induced pre-Lie algebra by symmetric solutions of the pre-Novikov Yang-Baxter equation in a pre-Novikov algebra. |
| title | Infinite-dimensional pre-Lie bialgebras via affinization of pre-Novikov bialgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2507.00492 |