Construction of free Lie Rota-Baxter superalgebra via Gr\"obner-Shirshov bases theory
Abstract
In this paper, we construct free Lie Rota-Baxter superalgebra by using Gr\"obner-Shirshov bases theory. We firstly construct free operated Lie superalgebras by the operated super-Lyndon-Shirshov monomials. Secondly, we establish Gr\"obner-Shirshov bases theory for operated Lie superalgebras. Thirdly, we find a Gr\"obner-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.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.