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arXiv · 1604.06675

Gr\"obner-Shirshov bases for Lie $\Omega$-algebras and free Rota-Baxter Lie algebras

Jianjun Qiu·Yuqun Chen
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Abstract

In this paper, we generalize the Lyndon-Shirshov words to Lyndon-Shirshov $\Omega$-words on a set $X$ and prove that the set of all non-associative Lyndon-Shirshov $\Omega$-words forms a linear basis of the free Lie $\Omega$-algebra on the set $X$. From this, we establish Gr\"{o}bner-Shirshov bases theory for Lie $\Omega$-algebras. As applications, we give Gr\"{o}bner-Shirshov bases for free $\lambda$-Rota-Baxter Lie algebras, free modified $\lambda$-Rota-Baxter Lie algebras and free Nijenhuis Lie algebras and then linear bases of such three free algebras are obtained.

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BibTeXRIS

Jianjun Qiu, Yuqun Chen. 2016-03-24. Gr\"obner-Shirshov bases for Lie $\Omega$-algebras and free Rota-Baxter Lie algebras. https://arxiv.org/abs/1604.06675

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