2016/03/24 by Jianjun Qiu, Qiu, Jianjun, Yuqun Chen +1
Mathematics · #13P10 #16S15 #16T25 #17A50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1604.06675
openalex publication_date 2016/03/24 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In this paper, we generalize the Lyndon-Shirshov words to Lyndon-Shirshov Ω-words on a set X and prove that the set of all non-associative Lyndon-Shirshov Ω-words forms a linear basis of the free Lie Ω-algebra on the set X. From this, we establish Gröbner-Shirshov bases theory for Lie Ω-algebras. As applications, we give Gröbner-Shirshov bases for free λ-Rota-Baxter Lie algebras, free modified λ-Rota-Baxter Lie algebras and free Nijenhuis Lie algebras and then linear bases of such three free algebras are obtained.