Is there any integer (Jones) index subfactor which is not extremal?
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2$\begingroup$ The $A_{\infty}^{(1)}$ subfactors, introduced by Vaughan Jones in his paper, realize every index $\ge 4$, and are non-extremal. See Remark 6.6 in this paper by Das-Ghosh-Gupta. See also mathoverflow.net/q/207806/34538 $\endgroup$– Sebastien PalcouxCommented Jun 25 at 2:27
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$\begingroup$ Thank you very much. $\endgroup$– Keshab BakshiCommented Jun 25 at 4:23
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$\begingroup$ @SebastienPalcoux Any other examples? $\endgroup$– Keshab BakshiCommented Jun 25 at 7:25
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1$\begingroup$ I guess you can get infinitely many examples by tensor product. To avoid such straightforward construction, we can request maximality. Eveything is explained in mathoverflow.net/q/207806/34538 $\endgroup$– Sebastien PalcouxCommented Jun 25 at 7:43
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$\begingroup$ I meant other type of examples. Note that commuting square subfactors will always be extremal. $\endgroup$– Keshab BakshiCommented Jun 25 at 8:17
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