Weak multiplier bialgebras

Böhm, Gabriella; Gómez-Torrecillas, José; Centella, Esperanza López

doi:10.1090/tran/6308

Cited by 23 publications

(190 citation statements)

References 10 publications

Supporting

Mentioning

190

Contrasting

Order By: Relevance

“…Moreover the notion of a measured multiplier Hopf algebroid (a regular multiplier Hopf algebroid with a faithful integral), as it is defined in Definition 2.2.1 in [19], involves some unexpected conditions (see e.g. condition (4) in that definition). Finally, remark that the duality of regular weak multiplier Hopf algebras as obtained in Section 5.1 of [19] is more involved than it looks at a first glance.…”

Section: The Place Of These Results In the Theorymentioning

confidence: 99%

See 1 more Smart Citation

On duality of algebraic quantum groupoids

Timmermann

2017

Advances in Mathematics

View full text Add to dashboard Cite

Algebraic quantum groupoids have been developed by two of the authors of this note (AVD and SHW) in a series of papers [34, 35, 36] and [37], see also [32]. By an algebraic quantum groupoid, we understand a regular weak multiplier Hopf algebra with enough integrals. Regular multiplier Hopf algebroids are obtained also by two authors of this note (TT and AVD) in [20]. Integral theory and duality for those have been studied by one author here (TT) in [18,19]. In these papers, the term algebraic quantum groupoid is used for a regular multiplier Hopf algebroid with a single faithful integral. Finally, again two authors of us (TT and AVD) have investigated the relation between weak multiplier Hopf algebras and multiplier Hopf algebroids in [21].(2) Address:

show abstract

Section: The Place Of These Results In the Theorymentioning

confidence: 99%

“…It was entitled The Larson Sweedler theorem for weak multiplier Hopf algebras. This work was inspired by the work of Böhm et al [4] on weak multiplier bialgebras that was available already in 2014. The Larson Sweedler paper appeared in 2018 (see [7]).…”

Section: Integral Theory and Dualitymentioning

confidence: 99%

On duality of algebraic quantum groupoids

Timmermann

2017

Advances in Mathematics

View full text Add to dashboard Cite

show abstract

“…Finally, assume that B χ B is an invertible character as in (4). Then the maps Θ λ := ρ( B χ B ) and Θ ρ := λ( B χ B ) are bijections of A because B χ B is invertible in the convolution algebra, and they are automorphisms because B χ B is a character.…”

Section: Modificationmentioning

confidence: 99%

“…The latter were introduced by Van Daele and the author in [18] and simultaneously generalize the regular weak multiplier Hopf algebras studied by Van Daele and Wang [24,19] and Böhm [4], and Hopf algebroids studied by [5,11,25], see also [2].…”

Section: Introductionmentioning

confidence: 96%

Integration on algebraic quantum groupoids

Timmermann

2016

Int. J. Math.

View full text Add to dashboard Cite

Abstract. In this article, we develop a theory of integration on algebraic quantum groupoids in the form of regular multiplier Hopf algebroids, and establish the main properties of integrals obtained by Van Daele for algebraic quantum groups beforefaithfulness, uniqueness up to scaling, existence of a modular element and existence of a modular automorphism -for algebraic quantum groupoids under reasonable assumptions. The approach to integration developed in this article forms the basis for the extension of Pontrjagin duality to algebraic quantum groupoids, and for the passage from algebraic quantum groupoids to operator-algebraic completions, which both will be studied in separate articles.

show abstract

“…Condition (C) says that the multiplication m for the multiplier bimonoid (t 1 , t 2 ) is related to the multiplication m for the multiplier bimonoid (t 3 , t 4 ) via the equation m = mb; this condition is self-dual. Thus (1) is equivalent to (2), and (3) is equivalent to (4). In applying the C-C duality, one must also replace m by m = mb −1 .…”

Section: Definition 38mentioning

confidence: 99%