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On Maximal Abelian Self–adjoint Subalgebras of Factors of Type II1

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Abstract

In this note, we show that if \({\fancyscript N}\)is a proper subfactor of a factor ℳ of type II1 with finite Jones index, then there is a maximal abelian self–adjoint subalgebra (masa) \({\fancyscript A}\)of \({\fancyscript N}\)that is not a masa in ℳ. Popa showed that there is a proper subfactor ℛ0 of the hyperfinite type II1 factor ℛ such that each masa in ℛ0 is also a masa in ℛ. We shall give a detailed proof of Popa's result.

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Authors and Affiliations

  1. Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, P. R. China

    Li Guang Wang

  2. Department of Mathematics, Qufu Normal University, Qufu 273165, P. R. China

    Li Guang Wang

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  1. Li Guang Wang
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Correspondence to Li Guang Wang.

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This work is supported by the National Natural Science Foundation of China (10301004)

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Wang, L.G. On Maximal Abelian Self–adjoint Subalgebras of Factors of Type II1 . Acta Math Sinica 21, 569–576 (2005). https://doi.org/10.1007/s10114-004-0460-x

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  • DOI: https://doi.org/10.1007/s10114-004-0460-x

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