Virtual Extension of Temperley--Lieb Algebra
  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. 
Yong Zhang (1), Louis H. Kauffman (2), Mo-Lin Ge (1) (1. Chern Inst.   Math., 2. Illinois at Chicago)