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Weighted infinitesimal unitary bialgebras on free monoid algebras

Volume 166 / 2021

Dan Chen, Yan-Feng Luo, Xiao-Song Peng, Yi Zhang Colloquium Mathematicum 166 (2021), 1-22 MSC: 16W99, 16T10, 17B60, 20M05. DOI: 10.4064/cm8123-6-2020 Published online: 8 January 2021

Abstract

The concept of a weighted infinitesimal unitary bialgebra is an algebraic abstraction of the non-homogeneous associative classical Yang–Baxter equation. In this paper, we equip the free monoid algebra with a suitable coproduct which makes it a weighted infinitesimal unitary bialgebra. Furthermore, by exploring the relationship between weighted infinitesimal unitary bialgebras and pre-Lie algebras, we construct a pre-Lie algebra on free monoid algebras. Finally, we show that the weighted infinitesimal unitary bialgebra on free monoid algebras has an infinitesimal unitary Hopf algebra structure in the sense of Aguiar.

Authors

  • Dan ChenSchool of Mathematics and Statistics
    Lanzhou University
    Lanzhou 730000, China
    e-mail
  • Yan-Feng LuoSchool of Mathematics and Statistics
    Lanzhou University
    Lanzhou 730000, China
    e-mail
  • Xiao-Song PengSchool of Mathematics and Statistics
    Lanzhou University
    Lanzhou 730000, China
    e-mail
  • Yi ZhangSchool of Mathematics and Statistics
    NUIST
    Nanjing 210044, China
    and
    School of Mathematics and Statistics
    Lanzhou University
    Lanzhou 730000, China
    e-mail

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