Cleft extensions of weak Hopf algebras

2018/11/07 by Guccione, Jorge A., Guccione, Juan J., Valqui, Christian
#16T05 (Primary) #18D10 (secondary) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1811.02909

Abstract

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.

Related

• Integrals and crossed products over weak Hopf algebras
• Cleft and Galois extensions associated to a weak Hopf quasigroup
• Crossed product and Galois extension of monoidal Hom-Hopf algebras
• Comparison of two notions of weak crossed product
• Crossed products and cleft extensions for coquasi-Hopf algebras