Virtual Extension of Temperley--Lieb Algebra

Zhang, Yong; Kauffman, Louis H.; Ge, Mo-Lin

Virtual Extension of Temperley--Lieb Algebra

Authors

Zhang, Yong

Kauffman, Louis H.

Ge, Mo-Lin

Description

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.
10 pages, latex