Multiplier Hopf algebroids: Basic theory and examples. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Timmermann, Thomas; Van Daele, Alfons
• Is Part Of: Communications in algebra. Volume 46:Issue 5(2018)
• Page Start: 1926
• Page End: 1958
• Publication Date: 2018-05-04
• Subjects: Bialgebroid -- Hopf algebroid -- quantum groupoid -- weak Hopf algebra; 16T05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1363220
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Multiplier Hopf algebroids are algebraic versions of quantum groupoids that generalize Hopf algebroids to the non-unital case and weak (multiplier) Hopf algebras to non-separable base algebras. The main structure maps of a multiplier Hopf algebroid are a left and a right comultiplication. We show that bijectivity of two associated canonical maps is equivalent to the existence of an antipode, discusses invertibility of the antipode, and presents some examples and special cases.