260 research outputs found
Subfactors of index less than 5, part 1: the principal graph odometer
In this series of papers we show that there are exactly ten subfactors, other
than subfactors, of index between 4 and 5. Previously this
classification was known up to index . In the first paper we give
an analogue of Haagerup's initial classification of subfactors of index less
than , showing that any subfactor of index less than 5 must appear
in one of a large list of families. These families will be considered
separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete
Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions
We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite
dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka
and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of
coideal subalgebras. We reduce the study to KD(n) by proving that the others
are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We
derive many examples of lattices of intermediate subfactors of the inclusions
of depth 2 associated to those Kac algebras, as well as the corresponding
principal graphs, which is the original motivation.
Along the way, we extend some general results on the Galois correspondence
for depth 2 inclusions, and develop some tools and algorithms for the study of
twisted group algebras and their lattices of coideal subalgebras. This research
was driven by heavy computer exploration, whose tools and methodology we
further describe.Comment: v1: 84 pages, 13 figures, submitted. v2: 94 pages, 15 figures, added
connections with Masuoka's families KA and KB, description of K3 in KD(n),
lattices for KD(8) and KD(15). v3: 93 pages, 15 figures, proven lattice for
KD(6), misc improvements, accepted for publication in Journal of Algebra and
Its Application
A confirmed case of toxic shock syndrome associated with the use of a menstrual cup
Menstrual cups have been reported to be an acceptable substitute for tampons. These flexible cups have also been reported to provide a sustainable solution to menstrual management, with modest cost savings and no significant health risk. The present article documents the first case of toxic shock syndrome associated with the use of a menstrual cup in a woman 37 years of age, using a menstrual cup for the first time. Toxic shock syndrome and the literature on menstrual cups is reviewed and a possible mechanism for the development of toxic shock syndrome in the patient is described
A confirmed case of toxic shock syndrome associated with the use of a menstrual cup
Menstrual cups have been reported to be an acceptable substitute for tampons. These flexible cups have also been reported to provide a sustainable solution to menstrual management, with modest cost savings and no significant health risk. The present article documents the first case of toxic shock syndrome associated with the use of a menstrual cup in a woman 37 years of age, using a menstrual cup for the first time. Toxic shock syndrome and the literature on menstrual cups is reviewed and a possible mechanism for the development of toxic shock syndrome in the patient is described
Rigid C^*-tensor categories of bimodules over interpolated free group factors
Given a countably generated rigid C^*-tensor category C, we construct a
planar algebra P whose category of projections Pro is equivalent to C. From P,
we use methods of Guionnet-Jones-Shlyakhtenko-Walker to construct a rigid
C^*-tensor category Bim whose objects are bifinite bimodules over an
interpolated free group factor, and we show Bim is equivalent to Pro. We use
these constructions to show C is equivalent to a category of bifinite bimodules
over L(F_infty).Comment: 50 pages, many figure
Open string theory and planar algebras
In this note we show that abstract planar algebras are algebras over the
topological operad of moduli spaces of stable maps with Lagrangian boundary
conditions, which in the case of the projective line are described in terms of
real rational functions. These moduli spaces appear naturally in the
formulation of open string theory on the projective line. We also show two
geometric ways to obtain planar algebras from real algebraic geometry, one
based on string topology and one on Gromov-Witten theory. In particular,
through the well known relation between planar algebras and subfactors, these
results establish a connection between open string theory, real algebraic
geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure
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