TY - JOUR
T1 - 1-Supertransitive Subfactors with Index at Most 6 1/5
AU - Liu, Zhengwei
AU - Morrison, Scott
AU - Penneys, David
N1 - Publisher Copyright:
© 2014, The Author(s).
PY - 2015/3
Y1 - 2015/3
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.
UR - http://www.scopus.com/inward/record.url?scp=84923230938&partnerID=8YFLogxK
U2 - 10.1007/s00220-014-2160-4
DO - 10.1007/s00220-014-2160-4
M3 - Article
SN - 0010-3616
VL - 334
SP - 889
EP - 922
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -