论文标题
辫子刚度为代数
Braid Rigidity for Path Algebras
论文作者
论文摘要
路径代数是描述张量类别中对象的张量功率分解的便捷方法。如果类别是编织的，则可以获得所有$ n \ in \ n $ in \ n $的编织组$ b_n $的表示。我们说，如果这些表示由路径代数和$ b_2 $的表示形式确定，则这些表示形式是严格的。我们表明，除了已知的经典案例外，还有$ g_2 $的7维表示路径代数的编织表示，但前提是$ b_3 $生成$ \ end $ \ end（v^{\ otimes 3}）$。如果满足此条件，我们将获得带有$ \ g（g_2）$的融合规则的功能张量类别的完整分类。
Path algebras are a convenient way of describing decompositions of tensor powers of an object in a tensor category. If the category is braided, one obtains representations of the braid groups $B_n$ for all $n\in \N$. We say that such representations are rigid if they are determined by the path algebra and the representations of $B_2$. We show that besides the known classical cases also the braid representations for the path algebra for the 7-dimensional representation of $G_2$ satisfies the rigidity condition, provided $B_3$ generates $\End(V^{\otimes 3})$. We obtain a complete classification of ribbon tensor categories with the fusion rules of $\g(G_2)$ if this condition is satisfied.
