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arXiv · 1809.06177

Rigid analytic quantum groups and quantum Arens-Michael envelopes

Nicolas Dupré
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Abstract

We introduce a rigid analytification of the quantized coordinate algebra of a semisimple algebraic group and a quantized Arens-Michael envelope of the enveloping algebra of the corresponding Lie algebra, working over a non-archimedean field and when $q$ is not a root of unity. We show that these analytic quantum groups are topological Hopf algebras and Fr\'echet-Stein algebras. We then introduce an analogue of the BGG category $\mathcal{O}$ for the quantum Arens-Michael envelope and show that it is equivalent to the category $\mathcal{O}$ for the corresponding quantized enveloping algebra.

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Nicolas Dupré. 2018-09-17. Rigid analytic quantum groups and quantum Arens-Michael envelopes. https://arxiv.org/abs/1809.06177

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