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arXiv · 2108.12281

Construction of free Lie Rota-Baxter superalgebra via Gr\"{o}bner-Shirshov bases theory

Jianjun Qiu·Yuqun Chen
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Abstract

In this paper, we construct free Lie Rota-Baxter superalgebra by using Gr\"{o}bner-Shirshov bases theory. We firstly construct free operated Lie superalgebras by the operated super-Lyndon-Shirshov monomials. Secondly, we establish Gr\"{o}bner-Shirshov bases theory for operated Lie superalgebras. Thirdly, we find a Gr\"{o}bner-Shirshov basis of a free Lie Rota-Baxter superalgebra on a $\mathbb{Z}_2$-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.

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Jianjun Qiu, Yuqun Chen. 2021-08-26. Construction of free Lie Rota-Baxter superalgebra via Gr\"{o}bner-Shirshov bases theory. https://arxiv.org/abs/2108.12281

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