Displaying similar documents to “Multiplier Hopf algebroids arising from weak multiplier Hopf algebras”

Weak multiplier Hopf algebras. Preliminaries, motivation and basic examples

Alfons Van Daele, Shuanhong Wang (2012)

Banach Center Publications

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Let G be a finite group. Consider the algebra A of all complex functions on G (with pointwise product). Define a coproduct Δ on A by Δ(f)(p,q) = f(pq) where f ∈ A and p,q ∈ G. Then (A,Δ) is a Hopf algebra. If G is only a groupoid, so that the product of two elements is not always defined, one still can consider A and define Δ(f)(p,q) as above when pq is defined. If we let Δ(f)(p,q) = 0 otherwise, we still get a coproduct on A, but Δ(1) will no longer be the identity in A ⊗ A....

On complements and the factorization problem of Hopf algebras

Sebastian Burciu (2011)

Open Mathematics

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Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well-known results from group theory. The uniqueness of a Krull-Schmidt-Remak type decomposition is proved for semisimple completely reducible Hopf algebras.

Smash (co)products and skew pairings.

José N. Alonso Alvarez, José Manuel Fernández Vilaboa, Ramón González Rodríguez (2001)

Publicacions Matemàtiques

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Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category γD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×] H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×] H is the Hopf algebra defined by Doi and Takeuchi. ...

The strong Morita equivalence for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras

Kazunori Kodaka, Tamotsu Teruya (2015)

Studia Mathematica

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Following Jansen and Waldmann, and Kajiwara and Watatani, we introduce notions of coactions of a finite-dimensional C*-Hopf algebra on a Hilbert C*-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rokhlin property for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras.

Multiplier Hopf algebras and duality

A. van Daele (1997)

Banach Center Publications

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We define a category containing the discrete quantum groups (and hence the discrete groups and the duals of compact groups) and the compact quantum groups (and hence the compact groups and the duals of discrete groups). The dual of an object can be defined within the same category and we have a biduality theorem. This theory extends the duality between compact quantum groups and discrete quantum groups (and hence the one between compact abelian groups and discrete abelian groups). The...

Hammerstein equations with an integral over a noncompact domain

Robert Stańczy (1998)

Annales Polonici Mathematici

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The existence of solutions of Hammerstein equations in the space of bounded and continuous functions is proved. It is obtained by the Schauder fixed point theorem using a compactness theorem. The result is applied to Wiener-Hopf equations and to ODE's.

Classifying bicrossed products of two Sweedler's Hopf algebras

Costel-Gabriel Bontea (2014)

Czechoslovak Mathematical Journal

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We continue the study started recently by Agore, Bontea and Militaru in “Classifying bicrossed products of Hopf algebras” (2014), by describing and classifying all Hopf algebras E that factorize through two Sweedler’s Hopf algebras. Equivalently, we classify all bicrossed products H 4 ⋈ H 4 . There are three steps in our approach. First, we explicitly describe the set of all matched pairs ( H 4 , H 4 , ▹ , ◃ ) by proving that, with the exception of the trivial pair, this set is parameterized by the ground field...