On weak group entwining structures

• Autores: Ling Jia, Fang Li
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 2, 2007, págs. 433-450
• Idioma: inglés
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• Resumen

  • Group coalgebras and Hopf group coalgebras appeared in the work of Turaev [1] on homotopy quantum field theories. A purely algebraic study of Hopf group coalgebras was initiated by Virelizer [2], and then continued by Scaenepeel and Wang [3]. Virelizer laid the algebraic foundations and gave a generalized version of the Fundamental Theorem for Hopf group coalgebras, Wang introduced the notions of a group entwining structure and of a group coalgebra extension, and Scaenepeel proposed an alternative approach to Hopf group coalgebras and showed that Hopf group coalgebras are essentially Hopf algebras in a symmetric monoidal category. We asked what the weak bialgebras in this category would be. We have found an answer to this question by introducing weak Hopf group coalgebras. This paper is devoted to studying the generalizations of entwining structure and coalgebra Galois extension in the setting of weak semi-Hopf group coalgebras, and have obtained a relation between them, that is, a weak group coalgebra Galois extension can induce a unique compatible weak group entwining structure.