1-Supertransitive Subfactors with Index at Most 6 1/5

Zhengwei Liu; Scott Morrison; David Penneys

doi:10.1007/s00220-014-2160-4

1-Supertransitive Subfactors with Index at Most 6 1/5

Zhengwei Liu, Scott Morrison^*, David Penneys

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

An irreducible II₁-subfactor (Formula presented.) is exactly 1-supertransitive if (Formula presented.) is reducible as an A − A bimodule. We classify exactly 1-supertransitive subfactors with index at most (Formula presented.), leaving aside the composite subfactors at index exactly 6 where there are severe difficulties. Previously, such subfactors were only known up to index (Formula presented.). Our work is a significant extension, and also shows that index 6 is not an insurmountable barrier. There are exactly three such subfactors with index in (Formula presented.), all with index (Formula presented.). One of these comes from SO(3)_q at a root of unity, while the other two appear to be closely related, and are ‘braided up to a sign’.

This is the published version of arXiv:1310.8566.

Original language	English
Pages (from-to)	889-922
Number of pages	34
Journal	Communications in Mathematical Physics
Volume	334
Issue number	2
DOIs	https://doi.org/10.1007/s00220-014-2160-4
Publication status	Published - Mar 2015

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title = "1-Supertransitive Subfactors with Index at Most 6 1/5",

abstract = "An irreducible II1-subfactor (Formula presented.) is exactly 1-supertransitive if (Formula presented.) is reducible as an A − A bimodule. We classify exactly 1-supertransitive subfactors with index at most (Formula presented.), leaving aside the composite subfactors at index exactly 6 where there are severe difficulties. Previously, such subfactors were only known up to index (Formula presented.). Our work is a significant extension, and also shows that index 6 is not an insurmountable barrier. There are exactly three such subfactors with index in (Formula presented.), all with index (Formula presented.). One of these comes from SO(3)q at a root of unity, while the other two appear to be closely related, and are {\textquoteleft}braided up to a sign{\textquoteright}.This is the published version of arXiv:1310.8566.",

author = "Zhengwei Liu and Scott Morrison and David Penneys",

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T1 - 1-Supertransitive Subfactors with Index at Most 6 1/5

AU - Liu, Zhengwei

AU - Morrison, Scott

AU - Penneys, David

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N2 - An irreducible II1-subfactor (Formula presented.) is exactly 1-supertransitive if (Formula presented.) is reducible as an A − A bimodule. We classify exactly 1-supertransitive subfactors with index at most (Formula presented.), leaving aside the composite subfactors at index exactly 6 where there are severe difficulties. Previously, such subfactors were only known up to index (Formula presented.). Our work is a significant extension, and also shows that index 6 is not an insurmountable barrier. There are exactly three such subfactors with index in (Formula presented.), all with index (Formula presented.). One of these comes from SO(3)q at a root of unity, while the other two appear to be closely related, and are ‘braided up to a sign’.This is the published version of arXiv:1310.8566.

AB - An irreducible II1-subfactor (Formula presented.) is exactly 1-supertransitive if (Formula presented.) is reducible as an A − A bimodule. We classify exactly 1-supertransitive subfactors with index at most (Formula presented.), leaving aside the composite subfactors at index exactly 6 where there are severe difficulties. Previously, such subfactors were only known up to index (Formula presented.). Our work is a significant extension, and also shows that index 6 is not an insurmountable barrier. There are exactly three such subfactors with index in (Formula presented.), all with index (Formula presented.). One of these comes from SO(3)q at a root of unity, while the other two appear to be closely related, and are ‘braided up to a sign’.This is the published version of arXiv:1310.8566.

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U2 - 10.1007/s00220-014-2160-4

DO - 10.1007/s00220-014-2160-4

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SN - 0010-3616

VL - 334

SP - 889

EP - 922

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -

1-Supertransitive Subfactors with Index at Most 6 1/5

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