Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.01614 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911248429350912 |
|---|---|
| author | Alhussein, H. |
| author_facet | Alhussein, H. |
| contents | It is known that if $A$ is a finite-dimensional unital algebra equipped with a Rota-Baxter operator $R$ of weight $λ$, then spectrum of $R$ is a subset of $\{0,-λ\}$. We are interested on finding all consequences of the Rota-Baxter relation and the relation of the form $R^k(R+λ{\rm id})^l = 0$. In 2024, H.~Qiu, S. Zheng, Y. Dan solved this problem for $k = l = 1$ and $λ\neq0$. We find a Gröbner-Shirshov basis of the ideal generated by these two relations in general case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gröbner-Shirshov bases of Rota-Baxter algebra of weight $λ$ with spectrum lying in $\{0,-λ\}$ Alhussein, H. Rings and Algebras It is known that if $A$ is a finite-dimensional unital algebra equipped with a Rota-Baxter operator $R$ of weight $λ$, then spectrum of $R$ is a subset of $\{0,-λ\}$. We are interested on finding all consequences of the Rota-Baxter relation and the relation of the form $R^k(R+λ{\rm id})^l = 0$. In 2024, H.~Qiu, S. Zheng, Y. Dan solved this problem for $k = l = 1$ and $λ\neq0$. We find a Gröbner-Shirshov basis of the ideal generated by these two relations in general case. |
| title | Gröbner-Shirshov bases of Rota-Baxter algebra of weight $λ$ with spectrum lying in $\{0,-λ\}$ |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2507.01614 |