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I was told that, if I understand correctly, that the enveloping algebra of semisimple Lie algebra admits one family of quantum deformation as Hopf algebra, which was proved by Drinfeld. Anyone can tell the reference about it?

A cocommutative Hopf algebra is equivalent to the associated tensor category of modules together with the forgetful functor. I would like to understand in general how to measure the quantum deformation of a tensor category. Any reference on it?

I guess in both cases, one should compute some kind of Hochild (co)homology?

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