Logarithmic Hennings invariants for restricted quantum ??(2)
Logarithmic Hennings invariants for restricted quantum ??(2)
复制标题
受限量子的对数亨宁斯不变量 ??(2)
DOI：
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发表时间：
2017
影响因子：
0.7
通讯作者：
Nathan Geer
中科院分区：
文献类型：
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作者：
A. Beliakova;C. Blanchet;Nathan Geer
我们构造了限制量子$mathfrak{sl}（2）$在2 mathsf {p}$次单位根处的Hennings型对数不变量.这个量子群$U$不是辫状的，而是可因子分解的。不变量定义为一对：一个3-流形$M$和一个着色链接$L $内$M$。链接$L$被分成两部分，由中心元素和跟踪类（或$0^{ ext{th}}$ Hochschild同调。我们的建设的两个主要成分是普遍不变的弦链接的值在张量的权力$U$，和修改后的跟踪介绍了第三作者与他的合作者和计算张量的权力的正规表示。我们的不变量是由Jun Murakami构造的对数不变量的有色扩展。
We construct a Hennings type logarithmic invariant for restricted quantum $mathfrak{sl}(2)$ at a $2mathsf{p}$-th root of unity. This quantum group $U$ is not braided, but factorizable. The invariant is defined for a pair: a 3-manifold $M$ and a colored link $L$ inside $M$. The link $L$ is split into two parts colored by central elements and by trace classes, or elements in the $0^{ ext{th}}$ Hochschild homology of $U$, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of $U$, and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami.