The Arens-Michael functor in noncommutative geometry is an analogue of the analytification functor in algebraic geometry: out of the ring of “algebraic functions” on a noncommutative affine scheme, it constructs the ring of “holomorphic functions” on it when viewed as a noncommutative complex analytic space. In this paper, we explicitly compute the Arens-Michael envelopes of the Jordan plane and the quantum enveloping algebra $U_q(\mathfrak{sl}(2))$ of $\mathfrak{sl}(2)$ for $|q|=1$.

约旦飞机和 $单位_{问} (sl（sl） (2))$

德米特里·佩德琴科

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