Programme of the Conference

The conference started at 10:30 on March 21 and ended at 17:00 on March 22. It was followed by the annual «Day of Algebra» at Caen on March 23. All talks were 45 minutes long and took place in Lecture Hall S3 043 on Campus 2. For lunch we used the self-service restaurant of the campus. For the diner of Wednesday 21 we met at 19:30 at the Café Mancel in the city center, see the page on practical informations. Here is the detailed programme:

• Y. Chapovskyi (Kiev) Compact quantum hypergroups slides of the talk.
• M.-C. David (Orsay) Examples: Kac algebras and intermediate subfactors slides of the talk.
• K. De Commer (Cergy) Podles spheres, quantum groupoids and special functions slides of the talk. We will explain how the non-standard Podles spheres lead to a family of quantum groupoids with a classical object set consisting of 2+1 points. The distinghuished point has the dual of quantum SU(2) as its isotropy group. Composition of arrows out of and into this distinghuished point leads to certain fusion rules between different Podles spheres, with values in the representation category of quantum SU(2). We show however that, on a purely algebraic level, the fusion rules are not well-defined, due to the indeterminateness of a moment problem involving q-inverse dual Hahn polynomials. This is joint work with E. Koelink.
• P. Fima (Paris) K-amenability of HNN-extensions of amenable discrete quantum groups
• A. Kalyuzhnyi (Kiev) Harmonic analysis on a locally compact hypergroup slides of the talk.
• D. Nikshych (New Hampshire) Arithmetic properties and classification of fusion categories and Hopf algebras
• G. B. Podkolzin (Kiev) On the group of extensions for the bicrossed product construction for a locally compact group slides of the talk.
• S. Vaes (Leuven) II_1 factors with a unique Cartan decomposition slides of the talk.
• J.-M. Vallin (Orléans) On examples of quantum groupoids and subfactors in relation with fusion categories
• A. Van Daele (Leuven) Algebraic quantum groupoids slides of the talk. For any finite groupoid G, the algebra K(G) of complex functions on G (with pointwise operations) is a (finite-dimensional) weak Hopf algebra for the coproduct Δ on K(G) defined as usual by Δ(f)(p,q)= f(pq) when p,q ∈ G and when pq is defined, and by Δ(f)(p,q) = 0 if pq is not defined. If the group G is no longer assumed to be finite, this result is no longer true. However, if we then take for K(G) the algebra of complex functions with finite support on G (again with pointwise operations), then Δ defined as above makes of the pair (K(G),Δ) a weak multiplier Hopf algebra with integrals.
  In this talk, I will first explain the notion of a weak multiplier Hopf algebra and discuss the relation with the known concept of a weak Hopf algebra. It is no longer assumed that the underlying algebra has an identity and it follows that one has to consider coproducts that map into the multiplier algebra of the tensor product K(G) ⊗ K(G) of K(G) with itself. Even more than in the case of multiplier Hopf algebras, this implies essential differences.
  In the second part of the talk, I will discuss the case where the weak multiplier Hopf algebra has integrals. Then it is possible to construct a dual, just as in the case of finite-dimensional weak Hopf algebras. The construction is similar as in the case of multiplier Hopf algebras with integrals. We call such a weak multiplier Hopf algebra an algebraic quantum groupoid. In the involutive case, and when the integrals are positive, it is expected to get a measured quantum groupoid as studied by Enock, Lesieur and others.
  This is about work in progress with Shuanhong Wang (Southeast University of Nanjing - China).
• S. L. Woronowicz (Warsaw) Multiplicative unitary for quantum codouble slides of the talk.

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