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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.

16W30 Hopf algebras (associative rings and algebras) (MSC2000)
16W35 Ring-theoretic aspects of quantum groups (MSC2000)
Full Text: DOI
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