The Hidden Group Structure of Quantum Groups: Strong Duality, Rigidity and Preferred Deformations

STRONG DUALITY, RIGIDITY AND PREFERRED DEFORMATIONS. P. BONNEAU 1 M. FLATO1, M. GERSTENHABER 2 and G. PINCZON 1 Abstract: A notion of well-behaved Hopf algebra is introduced; re exivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coe cients 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 coe cients and C1-functions. Strong rigidity (H2 bi = f0g) under deformations in the category of bialgebras is proved and consequences are deduced. AMS classi cation: Primary 17B37, 16W30, 22C05 46H99, 81R50. Running title : Topological quantum groups. (In press in Communications in Mathematical Physics, end of 1993)