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Gröbner-Shirshov bases for Rota-Baxter algebras

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Abstract

We establish the composition-diamond lemma for associative nonunitary Rota-Baxter algebras of weight λ. To give an application, we construct a linear basis for a free commutative and nonunitary Rota-Baxter algebra, show that every countably generated Rota-Baxter algebra of weight 0 can be embedded into a two-generated Rota—Baxter algebra, and prove the 1-PBW theorems for dendriform dialgebras and trialgebras.

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Authors and Affiliations

  1. South China Normal University, Guangzhou, P. R. China

    L.A. Bokut, Yu. Chen & X. Deng

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    L.A. Bokut

Authors
  1. L.A. Bokut
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  2. Yu. Chen
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  3. X. Deng
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Correspondence to L.A. Bokut.

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 1237–1250, November–December

Original Russian Text Copyright © 2010 Bokut L. A., Chen Yu., and Deng X.

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Bokut, L., Chen, Y. & Deng, X. Gröbner-Shirshov bases for Rota-Baxter algebras. Sib Math J 51, 978–988 (2010). https://doi.org/10.1007/s11202-010-0097-1

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