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Description

We define a notion of super-transitivity for etale algebras A in the modular tensor categories $C(sl_N, k)$. This is a direct analogue of the notion of super-transitivity for subfactors, and measure the depth at which the first new stuff appears in the category of A-modules. We will present a classification result for 1-super-transitive etale algebras. This classification result includes all but 14 of the currently known non-pointed etale algebras in $C(sl_N, k)$. These remaining etale algebras have super-transitivities between 2 and 4.