Integral Theory for Quasi-Hopf Algebras

Abstract

We generalize the fundamental structure Theorem on Hopf (bi)-modules by Larson and Sweedler to quasi-Hopf algebras H. If H is finite dimensional this proves the existence and uniqueness (up to scalar multiples) of integrals in H. Among other applications we prove a Maschke type Theorem for diagonal crossed products as constructed by the authors.

28 pages, amstex, formula at the end of section 6 corrected

References in corpus (2)

• A Coassociative C*-Quantum Group with Non-Integral Dimensions
• Weak Hopf Algebras I: Integral Theory and C^*-structure

Cited by in corpus (21)

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• An analogue of Radford's S^4 formula for finite tensor categories
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• Antipodes, preantipodes and Frobenius functors
• Hopf modules for autonomous pseudomonoids and the monoidal centre
• Hopf modules, Frobenius functors and (one-sided) Hopf algebras
• On the Structure Theorem for quasi-Hopf bimodules
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• From Projective Representations to Quasi-Quantum Groups
• On Categories associated to a Quasi-Hopf algebra
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• An approach to quasi-Hopf algebras via Frobenius coordinates
• Non-semisimple link and manifold invariants for symplectic fermions
• Preantipodes for dual-quasi bialgebras
• The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective
• A structure theorem for quasi-Hopf comodule algebras