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Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras

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Abstract

This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra, defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively. We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms. More significantly, Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras. Free totally compatible dialgebras are constructed. We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra, generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Yong Zhang

  2. Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, 300071, China

    ChengMing Bai

  3. Department of Mathematics, Lanzhou University, Lanzhou, 730000, China

    Li Guo

  4. Department of Mathematics and Computer Science, Rutgers University, Newark, NJ, 07102, USA

    Li Guo

Authors
  1. Yong Zhang
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  2. ChengMing Bai
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  3. Li Guo
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Correspondence to Li Guo.

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Zhang, Y., Bai, C. & Guo, L. Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras. Sci. China Math. 57, 259–273 (2014). https://doi.org/10.1007/s11425-013-4756-0

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  • DOI: https://doi.org/10.1007/s11425-013-4756-0

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