72 citations · 139 across the 19 of their papers we have counts for
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Single sided multiplier Hopf algebras
Alfons Van Daele
Let be a non-degenerate algebra over the complex numbers and a homomorphism from to the multiplier algebra . Consider the linear maps and fro…
Reflections on coproducts for non-unital algebras
Alfons Van Daele
A coproduct on a vector space is defined as a linear map satisfying coassociativity . We use for the identity map. If is…
Pairing and duality of algebraic quantum groupoids
T. Timmermann, A. Van Daele, S. H. Wang
Algebraic quantum groupoids have been developed by two of the authors (AVD and SHW) of this note in a series of papers. Regular multiplier Hopf algebroids are obtained also by two…
Weak multiplier Hopf algebras III. Integrals and duality
Alfons Van Daele, Shuanhong Wang
Let be a weak multiplier Hopf algebra. It is a pair of a non-degenerate algebra , with or without identity, and a coproduct on , satisfying certain properties. Th…
Modified weak multiplier Hopf algebras
Alfons Van Daele
Let be a regular weak multiplier Hopf algebra. Denote by the canonical idempotent of and by the image of the source map. Recall that is a non-degenerate…
Multiplier Hopf algebroids arising from weak multiplier Hopf algebras
Thomas Timmermann, Alfons Van Daele
It is well-known that any weak Hopf algebra gives rise to a Hopf algebroid. Moreover it is possible to characterize those Hopf algebroids that arise in this way. Recently, the noti…
The Larson-Sweedler theorem for weak multiplier Hopf algebras
Byung-Jay Kahng, Alfons Van Daele
The Larson-Sweedler theorem says that a finite-dimensional bialgebra with a faithful integral is a Hopf algebra. The result has been generalized to finite-dimensional weak Hopf alg…
Weak Multiplier Hopf Algebras II. The source and target algebras
Alfons Van Daele, Shuanhong Wang
In this paper, we continue the study of weak multiplier Hopf algebras. We recall the notions of the source and target maps and , as well as of the so…
Separability Idempotents and Multiplier Algebras
Alfons Van Daele
Consider two non-degenerate algebras B and C over the complex numbers. We study a certain class of idempotent elements E in the multiplier algebra of the tensor product of B with C…
Bicrossproducts of algebraic quantum groups
Lydia Delvaux, Alfons Van Daele, Shuanhong Wang
Let and be two algebraic quantum groups (i.e. multiplier Hopf algebras with integrals). Assume that is a right -module algebra and that is a left -comodule co…
Algebraic quantum groups II. Constructions and examples
L. Delvaux, A. Van Daele
Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct on A making it a multiplier Hopf algebra. In fac…
A note on Radford's formula
L. Delvaux, A. Van Daele, Shuanhong Wang
In this note, we show that Radford's formula for the fourth power of the antipode can be proven for any regular multiplier Hopf algebra with integrals (algebraic quantum groups). T…