2021/08/26 by Jianjun Qiu, Qiu, Jianjun, Yuqun Chen +1
Mathematics · #13P10 #16S15 #16T25 #16T25 17A50 #17A50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2108.12281
openalex publication_date 2021/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we construct free Lie Rota-Baxter superalgebra by using Gröbner-Shirshov bases theory. We firstly construct free operated Lie superalgebras by the operated super-Lyndon-Shirshov monomials. Secondly, we establish Gröbner-Shirshov bases theory for operated Lie superalgebras. Thirdly, we find a Gröbner-Shirshov basis of a free Lie Rota-Baxter superalgebra on a ℤ2-graded set. Consequently, we can obtain a linear basis of a free Lie Rota-Baxter superalgebra by the composition-diamond lemma for operated Lie superalgebras.