Frobenius Algebras, Q-Systems and Modules

  • Marcel Bischoff
  • Yasuyuki Kawahigashi
  • Roberto Longo
  • Karl-Henning Rehren
Chapter
First Online:
Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 3)

Abstract

We introduce the notion of Q-systems as Frobenius algebras in a C* tensor category, enjoying a standardness property. Q-systems in the category of endomorphisms of an infinite factor \(N\) completely characterize extensions \(N\subset M\). Modules and bimodules of Q-systems are equivalent to homomorphisms \(N\rightarrow M\) resp. \(M_1\rightarrow M_2\).

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Marcel Bischoff
    • 1
  • Yasuyuki Kawahigashi
    • 2
  • Roberto Longo
    • 3
  • Karl-Henning Rehren
    • 1
  1. 1.Institut Für Theoretische PhysikUniversität GöttingenGöttingenGermany
  2. 2.Department of Mathematical Sciences and Kavli IPMU (WPI)The University of TokyoTokyoJapan
  3. 3.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly

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