  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.
