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Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras

Author

Listed:
  • Ding-Guo Wang

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
    These authors contributed equally to this work.)

  • Xing Wang

    (School of Mathematics and Computer Application Technology, Jining University, Qufu 273155, China
    These authors contributed equally to this work.)

Abstract

In this paper, we introduce the concept of a generalized Hopf–Ore extension of a Hopf group-coalgebra and give the necessary and sufficient conditions for the Ore extension of a Hopf group-coalgebra to be a Hopf group-coalgebra. Moreover, an isomorphism theorem on generalized Hopf group-coalgebra Ore extensions is given and specific cases in a simple type called special Hopf group-coalgebra Ore extensions are also considered. Our results are generalizations of Hopf–Ore extensions on Hopf algebras and also are very useful to construct new Hopf group-coalgebras.

Suggested Citation

  • Ding-Guo Wang & Xing Wang, 2022. "Generalized Hopf–Ore Extensions of Hopf Group-Coalgebras," Mathematics, MDPI, vol. 10(7), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1167-:d:786571
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