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Pairing and quantum double of multiplier Hopf algebras. (English) Zbl 0993.16024
Pairings of regular multiplier Hopf (*-)algebras are defined and investigated. Such a pairing arises naturally from any multiplier Hopf algebra with integral and its dual. To any pairing of regular multiplier Hopf (*-)algebras $$A$$ and $$B$$ is associated a quantum double, which is also a regular multiplier Hopf (*-)algebra. If $$A$$ and $$B$$ have integrals, then so does the quantum double. This construction produces new examples of multiplier Hopf (*-)algebras.

##### MSC:
 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 17B37 Quantum groups (quantized enveloping algebras) and related deformations
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