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Twisted tensor coproduct of multiplier Hopf algebras. (English) Zbl 1071.16032
Let $$A$$ and $$B$$ be multiplier Hopf algebras, and let $$T$$ be a cotwisting map, i.e. $$T\colon A\otimes B\to B\otimes A$$ is an algebra isomorphism satisfying certain conditions. The author defines a comultiplication on the tensor product of algebras $$A\otimes B$$ making it a multiplier Hopf algebra, called a twisted tensor coproduct. Skew copairings are introduced for multiplier Hopf algebras, and a cotwisting map is associated to any skew copairing. If $$A$$ is an algebraic quantum group, i.e. a regular multiplier Hopf algebra with non-zero integrals, let $$\widehat A$$ be the dual algebraic quantum group and $$D=\widehat A\times A^{cop}$$ be the associated Drinfeld double, which is also an algebraic quantum group. The dual algebraic quantum group $$\widehat D$$ is characterized as a twisted tensor coproduct.

##### MSC:
 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 16W35 Ring-theoretic aspects of quantum groups (MSC2000)
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##### References:
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