From paths on graphs to quantum groupoids I

Robert Coquereaux (30/8/06)

We shall present and discuss the notion of essential paths on graphs (Ocneanu) and use this notion to define the (first) algebra structure on the quantum groupoid associated with a graph G (here, we shall take G to be a tree). This algebra is finite dimenional when G is of type ADE. We shall also discuss the relations between essential paths, representation theory of SU2, Temperlie - Lieb - Jones algebras and with the Gelfand - Ponomarev construction for quivers. Genralizations to SLn will also be discussed.

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Steve Lack

Last modified: Wed Sep 1 10:50:43 EST 1999