• On Pimsner-Popa bases

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019