On Pimsner Popa bases

Abstract

In this paper we examine bases for finite index inclusion of $I{I}_1$ 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 $I{I}_1$ 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).

arXiv comment20 pages