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SUBFACTORS OF INDEX LESS THAN 5, PART 4: VINES

DAVID PENNEYS

Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, CA 94720-3840, USA

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and

JAMES E. TENER

Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, CA 94720-3840, USA

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https://doi.org/10.1142/S0129167X11007641Cited by:15 (Source: Crossref)

Abstract

We eliminate 39 infinite families of possible principal graphs as part of the classification of subfactors up to index 5. A number-theoretic result of Calegari–Morrison–Snyder, generalizing Asaeda–Yasuda, reduces each infinite family to a finite number of cases. We provide algorithms for computing the effective constants that are required for this result, and we obtain 28 possible principal graphs. The Ostrik d-number test and an algebraic integer test reduce this list to seven graphs in the index range (4,5) which actually occur as principal graphs.

Keywords:

AMSC: 46L37, 18D10

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