Skein theory for the D_{2n} planar algebras

Details Skein theory for the D_{2n} planar algebras Skein theory for the D_{2n} planar algebras

2008-08-06

arxiv.org/abs/0808.0764v3

J. Pure Appl. Algebra 214 (2010), no. 2, 117--139.

Mathematics

Quantum Algebra

published version, minor changes, 34 pages.

Scientific paper

10.1016/j.jpaa.2009.04.010

We give a combinatorial description of the "$D_{2n}$ planar algebra", by giving generators and relations. This includes a direct proof that the relations are consistent, as well as a complete description of the associated tensor category and its principal graph. While we use the usual langauge of subfactor planar algebras, the entire argument is `skein-theoretic', and there is no functional analysis.

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