Categories of weight modules for unrolled restricted quantum groups at roots of unity
- 作者: Rupert M.1
-
隶属关系:
- Utah State University
- 期: 卷 86, 编号 6 (2022)
- 页面: 187-206
- 栏目: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133911
- DOI: https://doi.org/10.4213/im9234
- ID: 133911
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详细
Motivated by connections to the singlet vertex operator algebra in the$\mathfrak{g}=\mathfrak{sl}_2$ case, we study the unrolledrestricted quantum group $\overline{U}_q^{ H}(\mathfrak{g})$ for any finitedimensional complex simple Lie algebra $\mathfrak{g}$ at arbitrary roots ofunity with a focus on its category of weight modules. We show that thebraid group action naturally extends to the unrolled quantum groups andthat the category of weight modules is a generically semi-simple ribboncategory (previously known only for odd roots) with trivial Mügercenter and self-dual projective modules.
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