Type of Local von Neumann Algebras in Abelian Quantum Double Models

Abstract

We show that the local von Neumann algebra on convex areas of the frustration-free ground state of abelian quantum double models is of type II∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$II_\\infty $$\\end{document}.