Groupoïdes quantiques

Maltsiniotis, Georges

doi:10.1080/00927870008827035

Cited by 23 publications

(22 citation statements)

References 6 publications

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“…Our main goal is to develop an appropriate notion of a locally compact quantum groupoid, which would generalize the category of locally compact quantum groups. At the purely algebraic level, attempts in this direction have been around for some time, with works by Maltsiniotis [22] (when the unit space is commutative), Lu [21] ("Hopf algebroids"), Xu [38] ("quantum universal enveloping algebroids"), for instance. In a more operator algebraic setting, there is a work by Yamanouchi [39] ("generalized Kac algebras").…”

Section: Introductionmentioning

confidence: 99%

A class of C∗-algebraic locally compact quantum groupoids part I. Motivation and definition

Kahng

Daele

2018

Int. J. Math.

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In this series of papers, we develop the theory of a class of locally compact quantum groupoids, which is motivated by the purely algebraic notion of weak multiplier Hopf algebras. In this Part I, we provide motivation and formulate the definition in the C * -algebra framework. Existence of a certain canonical idempotent element is required and it plays a fundamental role, including the establishment of the coassociativity of the comultiplication. This class contains locally compact quantum groups as a subclass.

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Section: Introductionmentioning

confidence: 99%

A class of C∗-algebraic locally compact quantum groupoids part I. Motivation and definition

Kahng

Daele

2018

Int. J. Math.

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“…Then applying A ⊗ H to the above equality one obtains Eq. (11). It follows then that t b t a = a 0 b 0 #b 1 a 1 ; i.e., ρ A A → A ⊗ H op is an algebra map; hence A ρ A is an H op -comodule algebra as required.…”

Section: Braided Commutative Algebras and Bialgebroidsmentioning

confidence: 89%

Bialgebroids, ×A-Bialgebras and Duality

Brzeziński¹,

Militaru²

2002

Journal of Algebra

198

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“…Commutative Hopf algebroids were first studied in [65]. There were similar descriptions in [57]. In [54], the definitions were slightly modified in order to include noncommutative cases.…”

Section: Groupoids Bialgebroids and Hopf Algebroidsmentioning

confidence: 99%

Dynamical quantum groups—the super story

Karaali¹

2007

Contemporary Mathematics

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We review recent results in the study of quantum groups in the super setting. In particular, we provide an overview of results about solutions of the Yang-Baxter equations in the super setting and develop the super analog of the theory of dynamical quantum groups.1 Another beautiful reference with a more geometric flavor is [58]. Here, Manin develops projective algebraic geometry in the context of supermanifolds. In this note, we will need neither the strength nor the sophistication of the tools provided there.

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Groupoïdes quantiques

Cited by 23 publications

References 6 publications

A class of C∗-algebraic locally compact quantum groupoids part I. Motivation and definition

A class of C∗-algebraic locally compact quantum groupoids part I. Motivation and definition

Bialgebroids, ×A-Bialgebras and Duality

Dynamical quantum groups—the super story

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