Abstract
In this paper, we examine bases for finite index inclusion of II1 factors and connected inclusion of finite dimensional C ∗-algebras. These bases behave nicely with respect to basic construction towers. As applications we have studied automorphisms of the hyperfinite II1 factor R which are ‘compatible with respect to the Jones’ tower of finite dimensional C ∗-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).
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Acknowledgements
The author wishes to thank V. S. Sunder for many helpful discussions. He would also like to thank Vijay Kodiyalam for the proof of Lemma 3.1.
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Communicating Editor: B V Rajarama Bhat
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Bakshi, K.C. On Pimsner–Popa bases. Proc Math Sci 127, 117–132 (2017). https://doi.org/10.1007/s12044-016-0319-y
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DOI: https://doi.org/10.1007/s12044-016-0319-y