Uprolling Unrolled Quantum Groups

2020/05/26 by Creutzig, Thomas, Rupert, Matthew
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2005.12445

Abstract

We construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group U_q^H(\mfg) of a simple Lie algebra \mfg at roots of unity, and study their categories of local modules. We determine their simple modules and derive conditions for these categories being finite, non-degenerate, and ribbon. Motivated by numerous examples in the \mfg=\mathfraksl₂ case, we expect some of these categories to compare nicely to categories of modules for vertex operator algebras. We focus in particular on examples expected to correspond to the higher rank triplet vertex algebra W_Q(r) of Feigin and Tipunin \citeFT and the B_Q(r) algebras of \citeC1.

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