Pairing and quantum double of multiplier Hopf algebras. (English) Zbl 0993.16024

Drabant, Bernhard; Van Daele, Alfons

Algebr. Represent. Theory 4, No. 2, 109-132 (2001).

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.

Reviewer: Sorin Dascalescu (Safat)

MSC:

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

Keywords:

regular multiplier Hopf algebras; pairings; quantum doubles; integrals