2015/11/27 by Thomas Creutzig, Shashank Kanade, Andrew R. Linshaw · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Categorical variable #Combinatorics #Conformal map #Dimension (graph theory) #Discrete mathematics #Graph #Homotopy and Cohomology in Algebraic Topology #Indecomposable module #Mathematical analysis #Mathematics #Parameterized complexity #Pure mathematics #Simple (philosophy) #Vertex (graph theory) #math.QA #math.RT
paper · pdf · doi:10.1142/s0219199719500019
published as Commun. Contemp. Math. 22 (2020), no. 1, 1950001, 49 pp · 34 pages
arxiv created 2015/11/27 · openalex publication_date 2019/01/22 · crossref created 2019/01/22 · crossref issued 2019/02/15 · crossref published 2019/02/15 · crossref published-online 2019/02/15 · crossref published-print 2020/02/01 · arxiv updated 2020/05/13 · crossref deposited 2024/07/14 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/05
Let [Formula: see text] be a simple vertex operator algebra (VOA) and consider a representation category of [Formula: see text] that is a vertex tensor category in the sense of Huang–Lepowsky. In particular, this category is a braided tensor category. Let [Formula: see text] be an object in this category that is a simple current of order two of either integer or half-integer conformal dimension. We prove that [Formula: see text] is either a VOA or a super VOA. If the representation category of [Formula: see text] is in addition ribbon, then the categorical dimension of [Formula: see text] decides this parity question. Combining with Carnahan’s work, we extend this result to simple currents of arbitrary order. Our next result is a simple sufficient criterion for lifting indecomposable objects that only depends on conformal dimensions. Several examples of simple current extensions that are [Formula: see text]-cofinite and non-rational are then given and induced modules listed.