[hal-00348369] EXPLORATION OF FINITE-DIMENSIONAL KAC ALGEBRAS AND LATTICES OF INTERMEDIATE SUBFACTORS OF IRREDUCIBLE INCLUSIONS

We study two infinite families of finite dimensional Hopf (in fact Kac) algebras constructed by L. Vainerman: automorphism groups, self-duality, lattices of coidalgebras, relations between the two families, etc. We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. This research was driven by heavy computer exploration, whose tools and methodology we further describe.



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