Planar algebra

In mathematics, planar algebras first appeared in the work of Vaughan Jones on the standard invariant of a II1 subfactor.[1] They also provide an appropriate algebraic framework for many knot invariants (in particular the Jones polynomial), and have been used in describing the properties of Khovanov homology with respect to tangle composition.[2][3] Any subfactor planar algebra provides a family of unitary representations of Thompson groups.[4] Any finite group (and quantum generalization) can be encoded as a planar algebra.[1]

  1. ^ a b Vaughan F. R. Jones (1999), "Planar algebras, I", arXiv:math/9909027
  2. ^ "Dror Bar-Natan: Publications: Cobordisms". Math.toronto.edu. arXiv:math/0410495. doi:10.2140/gt.2005.9.1443. Retrieved 2016-11-20.
  3. ^ Bar-Natan, Dror (2005). "Khovanov's homology for tangles and cobordisms". Geometry & Topology. 9 (3): 1443–1499. arXiv:math/0410495. doi:10.2140/gt.2005.9.1443. S2CID 1247623.
  4. ^ Vaughan F. R. Jones (2017), "Some unitary representations of Thompson's groups F and T", J. Comb. Algebra, 1 (1): 1–44, arXiv:1412.7740, doi:10.4171/JCA/1-1-1, MR 3589908, S2CID 119631229