Virtual Extension of Temperley--Lieb Algebra
Mathematical Physics
2007-05-23 v1 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid group and call it the virtual Temperley--Lieb algebra which is an extension of the Temperley--Lieb algebra by adding the group algebra of the symmetrical group. We make a connection clear between the Brauer algebra and virtual Temperley--Lieb algebra, and show the algebra generated by permutation and its partial transpose to be an example for the virtual Temperley--Lieb algebra and its important quotients.
Keywords
Cite
@article{arxiv.math-ph/0610052,
title = {Virtual Extension of Temperley--Lieb Algebra},
author = {Yong Zhang and Louis H. Kauffman and Mo-Lin Ge},
journal= {arXiv preprint arXiv:math-ph/0610052},
year = {2007}
}
Comments
10 pages, latex