虚Temperley-Lieb代数中的投影
Projectors in the Virtual Temperley-Lieb Algebra
摘要：
给出了虚Temperley-Lieb代数中投影子的定义方法，推广了Temperley-Lieb代数中的Jones-Wenzl投影子.我们证明了投影机具有与Jones-Wenzl投影机相似的性质，并且包含一个与虚生成元有关的额外性质，即投影机与虚生成元的乘积不变.我们还证明了投影$f_n$在虚Temperley-Lieba代数$VTL_n(d)$中的公理性质的唯一性。最后，我们找到了$f_n$的系数，并给出了投影器$f_n$的显式公式。
英文摘要：
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 $f_n$ in terms of its axiomatic properties in the virtual Temperley-Lieba algebra $VTL_n(d)$. Finally, we find the coefficients of $f_n$ and give an explicit formula for the projector $f_n$.
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