2016/11/29 by Sven Möller · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Central charge #Current algebra #Discrete mathematics #Holomorphic function #Jordan algebra #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Operator algebra #Operator product expansion #Orbifold #Pure mathematics #Subalgebra #Vertex (graph theory) #Vertex operator algebra #math.QA #math.RT #msc:17B69
paper · pdf · doi:10.26083/tuprints-00017356
276 pages, LaTeX; Ph.D. thesis, some typos corrected
openalex publication_date 2016/11/29 · openalex created_date 2016/12/08 · arxiv created 2017/07/12 · arxiv updated 2021/02/10 · openalex updated_date 2026/08/05
In this thesis we develop an orbifold theory for a finite, cyclic group G acting on a suitably regular, holomorphic vertex operator algebra V. To this end we describe the fusion algebra of the fixed-point vertex operator subalgebra VG and show that VG has group-like fusion. Then we solve the extension problem for vertex operator algebras with group-like fusion. We use these results to construct five new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds, contributing to the classification of the V1-structures of suitably regular, holomorphic vertex operator algebras of central charge 24. As another application we present the BRST construction of ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight.