Equivalences for Weak Crossed Products |
| |
Authors: | J. M. Fernández Vilaboa A. B. Rodríguez Raposo |
| |
Affiliation: | 1. Departamento de álxebra, Universidad de Santiago de Compostela, Santiago de Compostela, Spain;2. Departamento de Matemáticas, Universidade da Coru?a, Escuela Politécnica Superior, Ferrol, Spain |
| |
Abstract: | In this article, we give a criterion that characterizes equivalent weak crossed products. By duality, we obtain a similar result for weak crossed coproducts and, as a consequence, we find the conditions that assures the equivalence between two weak crossed biproducts. As an application, we show that the main results proved by Panaite in [12 Panaite, F. (2014). Equivalent crossed products and cross product bialgebras. Commun. Algebr. 42:1937–1952.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] (see also [11 Panaite, F. (2012). Invariance under twisting for crossed products. Proc. Am. Math. Soc. 140:755–763.[Crossref], [Web of Science ®] , [Google Scholar]]), for Brzeziński's crossed products, admits a substantial reduction in the imposed conditions. |
| |
Keywords: | Equivalent crossed products Preunit Monoidal category Weak crossed product |
|
|