• On Pimsner-Popa bases

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/127/01/0117-0132

    • Keywords

       

      Subfactor; basic construction; connected inclusion; Pimsner-Popa bases.

    • Abstract

       

      In this paper, we examine bases for finite index inclusion of ${\rm II}_1$ factors and connected inclusion of finite dimensional $C^\ast$-algebras. These bases behave nicely with respect to basic construction towers. As applications we have studied automorphisms of the hyperfinite ${\rm II}_1$ factor $R$ which are ‘compatible with respect to the Jones’ tower of finite dimensional $C^\ast$-algebras’. As a further application, in both cases we obtain a characterization, in terms of bases, of basic constructions. Finally we use these bases to describe the phenomenon of multistep basic constructions (in both the cases).

    • Author Affiliations

       

      Keshab Chandra Bakshi1

      1. The Institute of Mathematical Sciences, Taramani, Chennai 600 113, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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