English

Projectors in the Virtual Temperley-Lieb Algebra

Geometric Topology 2021-03-23 v1

Abstract

We present a method of defining projectors in the virtual Temperley-Lieb algebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra. We show that the projectors have similar properties with the Jones-Wenzl projectors, and contain an extra property which is associated with the virtual generator elements, that is, the product of a projector with a virtual generator is unchanged. We also show the uniqueness of the projector fnf_n in terms of its axiomatic properties in the virtual Temperley-Lieba algebra VTLn(d)VTL_n(d). Finally, we find the coefficients of fnf_n and give an explicit formula for the projector fnf_n.

Cite

@article{arxiv.2103.11355,
  title  = {Projectors in the Virtual Temperley-Lieb Algebra},
  author = {Qingying Deng and Xian'an Jin and Louis H. Kauffman},
  journal= {arXiv preprint arXiv:2103.11355},
  year   = {2021}
}

Comments

24 pages,9 figures

R2 v1 2026-06-24T00:23:35.678Z