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arXiv · 1301.5018

Gröbner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras

Jianjun Qiu
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Abstract

In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gröbner-Shirshov bases and linear bases of free commutative Rota-Baxter algebra, free commutative $λ$-differential algebra and free commutative $λ$-differential Rota-Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative $Ω$-words.

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Jianjun Qiu. 2013-01-18. Gröbner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras. https://arxiv.org/abs/1301.5018

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