Grobner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras ∗†

By Leonid A. Bokut, Yuqun Chen, Jianjun Qiu. 2008

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Abstract In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Grobner–Shirshov bases of free Rota–Baxter algebra, free λ -differential algebra and free λ -differential Rota–Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar to the recent results obtained by K. Ebrahimi-Fard–L. Guo, and L. Guo–W. Keigher by using other methods.

Subfields: Algebra and Number Theory, Geometry and Topology

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