Cleft extensions of weak Hopf algebras

Jorge A. Guccione, Juan J. Guccione, Christian Valqui

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf algebra, then the categories of H-cleft extensions of an algebra A, and of unitary crossed products of A by H, are equivalent.

Original languageEnglish
Pages (from-to)668-710
Number of pages43
JournalJournal of Algebra
StatePublished - 1 Apr 2020


  • Cleft extension
  • Symmetric categories
  • Weak Hopf algebras
  • Weak crossed product


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