Multiplier Hopf algebras and duality

A. van Daele

Displaying similar documents to “Multiplier Hopf algebras and duality”

Braided Groups

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Recherche Coopérative sur Programme n°25

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Twisted quantum doubles.

Fukuda, Daijiro, Kuga, Ken'ichi (2004)

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Preface, Contents

(1997)

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On the problem of classifying simple compact quantum groups

Shuzhou Wang (2012)

Banach Center Publications

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We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.

Deformed commutators on comodule algebras over coquasitriangular Hopf algebras

Zhongwei Wang, Guoyin Zhang, Liangyun Zhang (2015)

Colloquium Mathematicae

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We construct quantum commutators on comodule algebras over coquasitriangular Hopf algebras, so that they are quantum group coinvariant and have the generalized antisymmetry and Leibniz properties. If the coquasitriangular Hopf algebra is additionally cotriangular, then the quantum commutators satisfy a generalized Jacobi identity, and turn the comodule algebra into a quantum Lie algebra. Moreover, we investigate the projective and injective dimensions of some Doi-Hopf modules over a...

Hopf structures on the Borel subalgebra of $s l (2)$

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Problems in the theory of quantum groups

Shuzhou Wang (1997)

Banach Center Publications

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This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.

Amenability and coamenability of algebraic quantum groups.

Bédos, Erik, Murphy, Gerard J., Tuset, Lars (2002)

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Multiplier Hopf algebroids arising from weak multiplier Hopf algebras

Thomas Timmermann, Alfons Van Daele (2015)

Banach Center Publications

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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 notion of a weak Hopf algebra has been extended to the case of algebras without identity. This led to the theory of weak multiplier Hopf algebras. Similarly also the theory of Hopf algebroids was recently developed for algebras without identity. They are called multiplier Hopf algebroids. Then...

Examples of quantum braided groups

Hlavatý, Ladislav

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Summary: The author gives the defining relations of a new type of bialgebras that generalize both the quantum groups and braided groups as well as the quantum supergroups. The relations of the algebras are determined by a pair of matrices $(R, Z)$ that solve a system of Yang-Baxter-type equations. The matrix coproduct and counit are of standard matrix form, however, the multiplication in the tensor product of the algebra is defined by virtue of the braiding map given by the matrix $Z$ . Besides...