We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of $\mathfrak{sl_2}$ using purely combinatorial methods based on Temperley–Lieb algebras and Kauffman bracket polynomials. These invariants can be understood as a first-order extension of Witten–Reshetikhin–Turaev invariants, which can be reformulated following our approach in the case of rational homology spheres.

中文翻译：

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从考夫曼括号派生的非半简单 3 流形不变量

我们使用基于 Temperley-Lieb 代数和 Kauffman 括号多项式的纯组合方法来恢复与 $\mathfrak{sl_2}$ 的小量子群相关的封闭定向 3 流形的非半简单量子不变量族。这些不变量可以理解为 Witten-Reshetikhin-Turaev 不变量的一阶扩展，在有理同调领域的情况下，可以按照我们的方法重新制定。