Rigid analytic quantum groups and quantum Arens-Michael envelopes

2018/09/17 by Dupré, Nicolas
#FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1809.06177

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 Fréchet-Stein algebras. We then introduce an analogue of the BGG category O for the quantum Arens-Michael envelope and show that it is equivalent to the category O for the corresponding quantized enveloping algebra.

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