Uprolling unrolled quantum groups - Creutzig, Thomas; Rupert, Matthew (Communications in Contemporary Mathematics, 2022)
We construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group ŪqH() of a simple Lie algebra 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 = 2 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 WQ(r) of Feigin and Tipunin and the BQ(r) algebras.
CRIS-Team Scopus Importer:2024-06-24
Keywords: Algebra objects; Quantum groups; Vertex operator algebras