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Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras |
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| Authors: | LA Bokut Yuqun Chen Jianjun Qiu |
| Institution: | a School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China b Sobolev Institute of Mathematics, Russian Academy of Sciences, Siberian Branch, Novosibirsk 630090, Russia c Mathematics and Computational Science School, Zhanjiang Normal University, Zhanjiang 524048, PR China |
| Abstract: | In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Gröbner-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. |
| Keywords: | 16S15 13P10 16W99 17A50 |
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