Notes on the quantum tetrahedron by R. Coquereaux

This week I have been studying quite a complicated paper by Coquereaux. In this is paper the author describes several aspects of the space of paths on ADE Dynkin diagrams, particularly the graph E6 – the polytope corresponding to the E6 Lie algebra by the McKay correspondence is the 3-dimensional tetrahedron.

He looks at the  concept of essential matrices or intertwiners for a graph and describe their module properties with respect to right and left actions of fusion algebras. In the case of the graph E6, he finds that the essential matrices build up a right module with respect to its own fusion algebra but a left module with respect to the fusion algebra of A11. The author also presents a simple construction for the Ocneanu graph which describes the quantum symmetries of the Dynkin diagram E6.



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