On the double crossed product of weak Hopf algebras

Böhm, Gabriella Eszter and Gomez-Torrecillas, J. (2013) On the double crossed product of weak Hopf algebras. CONTEMPORARY MATHEMATICS, 585. pp. 153-173. ISSN 0271-4132

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Abstract

Given a weak distributive law between algebras underlying two weak bialgebras, we present sufficient conditions under which the corresponding weak wreath product algebra becomes a weak bial- gebra with respect to the tensor product coalgebra structure. When the weak bialgebras are weak Hopf algebras, then the same conditions are shown to imply that the weak wreath product becomes a weak Hopf algebra, too. Our sufficient conditions are capable to describe most known examples, (in particular the Drinfel’d double of a weak Hopf algebra) .

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