Handlebody-knot invariants derived from unimodular Hopf algebras
Handlebody-knot invariants derived from unimodular Hopf algebras
复制标题
从幺模 Hopf 代数导出的 Handlebody-knot 不变量
DOI：
10.1142/s0218216514600013
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Akira Masuoka
中科院分区：
文献类型：
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作者：
Atsushi Ishii;Akira Masuoka
为了系统地构造手柄体链接的不变量，我们通过生成器和关系给出了手柄体缠结的编织张量范畴的新表示，并证明给定任意编织张量范畴中的量子交换量子对称代数 A，会出现一个编织张量函子，它会产生所需的不变量。特别是当 A 是有限维幺模 Hopf 代数时，不变量的一些性质和显式计算结果得到了体现，它自然被视为 Yetter-Drinfeld 模编织张量范畴中的量子交换量子对称代数。
To systematically construct invariants of handlebody-links, we give a new presentation of the braided tensor categoryof handlebody-tangles by generators and relations, and prove that given what we call a quantum-commutative quantum-symmetric algebra A in an arbitrary braided tensor category, there arises a braided tensor functor, which gives rise to a desired invariant. Some properties of the invariants and explicit computational results are shown especially when A is a finite-dimensional unimodular Hopf algebra, which is naturally regarded as a quantum-commutative quantum-symmetric algebra in the braided tensor categoryof Yetter–Drinfeld modules.