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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Iterating the basic construction


Authors: Mihai Pimsner and Sorin Popa
Journal: Trans. Amer. Math. Soc. 310 (1988), 127-133
MSC: Primary 46L35
MathSciNet review: 965748
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Abstract: Let $ N \subset M$ be a pair of type II$ _{1}$ factors with finite Jones' index and $ N \subset M \subset {M_1} \subset {M_2} \subset \cdots \subset {M_n} \subset \cdots \subset {M_{2n + 1}}$ be the associated tower of type II$ _{1}$ factors obtained by iterating Jones' basic construction. We give an explicit formula of a projection in $ {M_{2n + 1}}$ which implements the conditional expectation of $ {M_n}$ onto $ N$, thus showing that $ {M_{2n + 1}}$ comes naturally from the basic construction associated to the pair $ N \subset {M_n}$. From this we deduce several properties of the relative commutant $ N' \cap {M_n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0965748-8
PII: S 0002-9947(1988)0965748-8
Article copyright: © Copyright 1988 American Mathematical Society



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