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Let $ U_q(\mathfrak{g})$ (defined over $ \mathbb{C}(q)$ ) be the quantized universal enveloping algebra of a simple Lie algebra $ \mathfrak{g}$ . Let $ M$ a finite-dimensional simple left $ U_q(\mathfrak{g})$ -module. Is it true that $ \dim_{\mathbb{C}(q)}\mathrm{End}_{U_q(\mathfrak{g})}(M)=1$ ? How to sketch a proof? The problem is that the field $ \mathbb{C}(q)$ is not algebraicallyRead more

I was told that the following equation is true: Given a finitely generated Lie algebra $ \mathfrak g$ , there is a Gerstenhaber algebra isomorphism $ $ HH(U\mathfrak g) \cong HH(\wedge^* \mathfrak g^\vee, \delta_{CE})$ $ where $ U\mathfrak g$ is the universal enveloping algebra, $ \wedge^* \mathfrak g^\vee$ is the dual of exterior algebra ofRead more