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Abstract
Weak crossed products by a weak bialgebra are defined. The resulting structure is not that of a unital algebra but an associative algebra with preunit. A general formula of such a product is given in terms of a weak 2-cocycle and a weak measuring. The relation with weak cleft extensions is studied. Equivalences of weak crossed products are defined and are related to gauge transformations. A relation between cleaving maps is described in terms of gauge transformations.
ACKNOWLEDGMENTS
The author would like to thank Tomasz Brzeziński for helpful discussions and Gabriella Böhm for her helpful comments. She would also like to thank the referee for the valuable comments. This article was written while the author was visiting the Department of Mathematics of the University of Wales-Swansea supported by Universidade de Santiago de Compostela. She is also supported by Ministerio de Ciencia y Tecnología, by Xunta de Galicia and by FEDER, Projects: BFM2003-07353-C02-01, PGIDITO4PXIC32202PN.
Notes
Communicated by H.-J. Schneider.