Projectors in the Virtual Temperley-Lieb Algebra

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 fn in terms of its axiomatic properties in the virtual Temperley-Lieba algebra V T Ln(d). Finally, we find the coefficients of fn and give an explicit formula for the projector fn.