Projectors in the Virtual Temperley-Lieb Algebra

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 TLn(d). Finally, we find the coefficients of fn and give an explicit formula for the projector fn. keywords : virtual Temperley-Lieb algebra; projector; recurrence formula; coefficient. Corresponding author

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