Gröbner-Shirshov bases for Lie Ω-algebras and free Rota-Baxter Lie algebras
Qiu, Jianjun · Chen, Yuqun
Original · EN
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.
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