1-supertransitive subfactors with index at most 6+1/5
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Liu, Zhengwei; Morrison, Scott; Penneys, David
Description
We classify irreducible II_1 subfactors A \subset B such that B \ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6. Previous work has already achieved this up to index 3+\sqrt{5} \approx 5.23. We find there are exactly three such subfactors with index in (3+\sqrt{5}, 6+1/5], all with index 3+2\sqrt{2}. 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...[Show more]
dc.contributor.author | Liu, Zhengwei | |
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dc.contributor.author | Morrison, Scott | |
dc.contributor.author | Penneys, David | |
dc.date.accessioned | 2014-04-16T02:36:54Z | |
dc.identifier.issn | 0010-3616 | |
dc.identifier.uri | http://hdl.handle.net/1885/11574 | |
dc.description.abstract | We classify irreducible II_1 subfactors A \subset B such that B \ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6. Previous work has already achieved this up to index 3+\sqrt{5} \approx 5.23. We find there are exactly three such subfactors with index in (3+\sqrt{5}, 6+1/5], all with index 3+2\sqrt{2}. 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'. | |
dc.format | 27 pages | |
dc.publisher | Springer Verlag | |
dc.rights | http://www.sherpa.ac.uk/romeo/issn/0010-3616/author can archive pre-print (ie pre-refereeing); author can archive post-print (ie final draft post-refereeing); on any open access repository after 12 months from publication; author cannot archive publisher's version/PDF | |
dc.source | Communications in Mathematical Physics | |
dc.subject | Operator Algebras (math.OA) | |
dc.subject | Quantum Algebra (math.QA) | |
dc.title | 1-supertransitive subfactors with index at most 6+1/5 | |
dc.type | Journal article | |
local.identifier.citationvolume | 334 | |
dc.date.issued | 2014 | |
local.identifier.absfor | 010103 - Category Theory, K Theory, Homological Algebra | |
local.identifier.absfor | 010108 - Operator Algebras and Functional Analysis | |
local.identifier.absfor | 010112 - Topology | |
local.identifier.ariespublication | a383154xPUB2866 | |
local.publisher.url | http://www.springerlink.com/?MUD=MP | |
local.type.status | Accepted Version | |
local.contributor.affiliation | Morrison, Scott, College of Physical and Mathematical Sciences, The Australian National University | |
local.description.embargo | Embargo: 2015-06-01 | |
dc.relation | http://purl.org/au-research/grants/arc/DE120100232 | |
dc.relation | http://purl.org/au-research/grants/arc/DP140100732 | |
local.bibliographicCitation.issue | 2 | |
local.bibliographicCitation.startpage | 889 | |
local.bibliographicCitation.lastpage | 922 | |
local.identifier.doi | 10.1007/s00220-014-2160-4 | |
dc.date.updated | 2016-06-14T08:31:47Z | |
local.identifier.scopusID | 2-s2.0-84923230938 | |
Collections | ANU Research Publications |
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