Multiplier Hopf algebroids. Basic theory and examples

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, discuss invertibility of the antipode, and present some examples and special cases.

now covers the non-regular case; to appear in Comm. in Algebra

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Cited by in corpus (1)

• Regular multiplier Hopf algebroids II. Integration on and duality of algebraic quantum groupoids