Questions tagged [planar-algebras]
The planar-algebras tag has no usage guidance.
57 questions
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Invertibility of the planar algebra-subfactor correspondence
In Jones's paper "Planar Algebras I", Theorem 4.2.1 establishes that an extremal finite index subfactor admits a spherical C*-planar algebra structure, and Theorem 4.3.1 establishes that spherical C*-...
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What are some natural and attractive open problems in Jones's theory of planar algebras?
I'm hoping to learn something about planar algebras while attacking a planar algebra question with an undergrad research student. I'm thinking about reading this paper, as Kuperberg's program seems ...
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Which presentations of (non)planar algebras give rise to knots?
Reidermeister's theorem states that the set of knots, modulo ambient isotopy, is isomorphic to the planar algebra generated by crossings, modulo Reidemeister moves. This planar algebra presentation is ...
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Why are fusion categories interesting?
In the same vein as Kate and Scott's questions, why are fusion categories interesting? I know that given a "suitably nice" fusion category (which probably means adding adjectives such as "unitary," "...
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ubiquity, importance of path algebras
I work in planar algebras and subfactors, where the idea of path algebras on a graph (alternately known as graph algebras, graph planar algebras, etc.) is quite useful. The particular result I'm ...
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Which computer algebra system should I be using to solve large systems of sparse linear equations over a number field?
This is related to Noah's recent question about solving quadratics in a number field, but about an even earlier and easier step.
Suppose I have a huge system of linear equations, say ~10^6 equations ...
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Short Introduction to Planar Algebras
Are there any good short expositions of planar algebras out there? I am interested primarily in seeing the main definition and some explicit examples.
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