In the first answer for this [question](https://mathoverflow.net/questions/5538/why-drinfeld-jimbo-type-quantum-groups) is writen, about the braided category of representation of the enveloping algebra $U(\frak{g})$, for $\frak{g}$ a semisimple Lie algebra: 



> 
> The space of deformations of the braided tensor structure on these particular categories is one dimensional (I believe this is a result of Drinfeld), so we get a universal family of braided deformations of U(g)-mod by varying q in U\_q(g). 
> 
> 
> 


What is the precise reference for this result? I guess here by tensor, the answerer means equivalently monoidal?


What happend if we take out "braided"? Does there exist deformations of the monoidal category of $U(\frak{g})$-modules which are not equivalent to the cateogry of modules of $U\_q(\frak{g})$, for some $q$?



Quantum groups and deformations of the monoidal category of $U(\frak{g})$-modules
That the only monoidal deformations of the category of representations of $U(\mathfrak{g})$ is the category of representations of $U\_q(\mathfrak{g})$ is known in Type A from Kazhdan-Wenzl (Adv. Soviet Math, 1993), for the category of vector representations in Type BCD by combining results of [Wenzl-Tuba](https://arxiv.org/abs/math/0301142) with [Liu](https://arxiv.org/abs/1507.06030), and for $G\_2$ by [Kuperberg](https://arxiv.org/abs/math/9201302). It is open for the other exceptional Lie algebras. I think it's open in type BD if you include the spin representations, though Wenzl has some partial results.


