A maschke type theorem for weak Hopf algebras |
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| Authors: | J N Alonso Álvarez J M Fernández Vilaboa R González Rodríguez A B Rodríguez Raposo |
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| Institution: | (1) Departamento de Matemáticas, Universidad de Vigo., Lagoas-Marcosende, Vigo., E-36200, Spain;(2) Departamento de álxebra, Universidad de Santiago de Compostela, Santiago de Compostela, E-15771, Spain;(3) Departamento de Matemática Aplicada II, Universidad de Vigo., Lagoas-Marcosende, Vigo., E-36310, Spain;(4) Departamento de álxebra, Universidad de Santiago de Compostela, Santiago de Compostela, E-15771, Spain |
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| Abstract: | In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total
integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce
a version of Maschke’s Theorem for (H,B)-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.
The authors have been supported by Ministerio de Educación y Ciencia Projects MTM2006-14908-C02-01, MTM2007-62427 and by FEDER |
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| Keywords: | Monoidal category weak Hopf algebra Hopf modules Maschke Theorem |
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