Lower and Upper Bounds for Positive Bases of Skein Algebras
Lower and Upper Bounds for Positive Bases of Skein Algebras
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DOI：
10.1093/imrn/rnaa082
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发表时间：
2019-08
影响因子：
1
通讯作者：
Thang T. Q. Lê;D. Thurston;Tao Yu
中科院分区：
文献类型：
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作者：
Thang T. Q. Lê;D. Thurston;Tao Yu
我们证明了，如果一个归一化多项式序列产生曲面的skein代数的正基，则它被夹在两类切比雪夫多项式之间。对于闭环面，我们证明了第一类切比雪夫多项式的归一化序列$(\hat{T}_n)$是唯一给出正基的序列。
We show that if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one $(\hat{T}_n)$ is the only one that gives a positive basis.