## From paths on graphs to quantum groupoids II

### Robert Coquereaux – 30 August 2006

In the second talk, we shall construct explicitly the second algebra structure on the (dual of the) quantum groupoid associated with a graph G, for the same type of graphs that we considered in Part-1. We shall do this by usiing explicit expressions for the generalized quantum 6J symbols. We shall also see that the algebra we end up with is weak (in the sense that the coproduct of the identity is not equal to the tensor square of the identity) but that it admits nice generalizations for the notions of coproduct and antipode.

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