2016/05/18 by Thomas Creutzig, Creutzig, Thomas, Antun Milas +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #hep-th #math.GT #math.NT #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.1605.05634
arxiv created 2016/05/18 · openalex publication_date 2016/05/18 · arxiv updated 2016/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study relationships between the restricted unrolled quantum group UqH(\mathfraksl2) at 2r-th root of unity q=eπi/r, r ≥ 2, and the singlet vertex operator algebra \mathcal M(r). We use deformable families of modules to efficiently compute (1, 1)-tangle invariants colored with projective modules of UqH(\mathfraksl2). These relate to the colored Alexander tangle invariants studied in [ADO, M1]. It follows that the regularized asymptotic dimensions of characters of \mathcal M(r) coincide with the corresponding modified traces of open Hopf link invariants. We also discuss various categorical properties of \mathcal M(r)-mod in connection to braided tensor categories.