2025/07/02 by H. Alhussein, Alhussein, H.
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2507.01614
openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Rk(R+λ\rm id)l = 0. In 2024, H.~Qiu, S. Zheng, Y. Dan solved this problem for k = l = 1 and λ≠0. We find a Gröbner-Shirshov basis of the ideal generated by these two relations in general case.