2003/06/30 by Sebastiano Carpi · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Central charge #Dimension (graph theory) #Net (polyhedron) #Random Matrices and Applications #Representation (politics) #Representation theory #Subnet #Virasoro algebra #Von Neumann architecture #math-ph #math.MP #math.OA
paper · pdf · doi:10.1007/s00220-003-0988-0
published as Commun. Math. Phys. 244, 261-284 (2004) · 34 pages
arxiv created 2003/06/30 · openalex publication_date 2004/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local extensions of the c=1 Virasoro net for which the restriction of the vacuum representation to the Virasoro subnet is a direct sum of irreducible subrepresentations with finite statistical dimension (local extensions of compact type). Moreover we prove that if the central charge c is in a certain subset of (1,∞), including [2,∞), and h ≥ (c-1)/24, the irreducible representation with lowest weight h of the corresponding Virasoro net has infinite statistical dimension. As a consequence we show that if the central charge c is in the above set and satisfies c≤ 25 then the corresponding Virasoro net has no proper local extensions of compact type.