93-321 Bonneau P., Flato M., Gerstenhaber M., Pinczon G.

The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations. (130K, plain TeX) Dec 4, 93

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Abstract. A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients and $C^\infty$-functions. Strong rigidity ($H^2_{bi} = \{ 0 \}$) under deformations in the category of bialgebras is proved and consequences are deduced.

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