三价图的Kauffman括号的完整性
Integrality of Kauffman brackets of trivalent graphs
摘要：
我们表明，考夫曼括号的有色框架图（也被称为量子自旋网络）可以重整为一个劳伦多项式与整数系数乘以一个系数，这是一个产品的量子因子只依赖于抽象的组合结构的图形。然后比较了基于$R$ -矩阵和Clebsch-Gordan符号的状态和与影子状态和的等价性，并对状态权的完整性进行了评论。我们还提供了简短的证明，满足大多数的标准身份的量子$6j$ -符号的$U_q(sl_2)$。
英文摘要：
We show that Kauffman brackets of colored framed graphs (also known as quantum spin networks) can be renormalized to a Laurent polynomial with integer coefficients by multiplying it by a coefficient which is a product of quantum factorials depending only on the abstract combinatorial structure of the graph. Then we compare the shadow-state sums and the state-sums based on $R$-matrices and Clebsch-Gordan symbols, reprove their equivalence and comment on the integrality of the weight of the states. We also provide short proofs of most of the standard identities satisfied by quantum $6j$-symbols of $U_q(sl_2)$.
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