Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.01614 |
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Sommario:
- 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.