论文标题
集成性和编织张量类别
Integrability and braided tensor categories
论文作者
论文摘要
许多可集成的统计机械模型都具有分数旋转电流。这些电流是通过利用量子组代数和“离散全态性”的想法来构建的。我发现它们自然而然地使用了编织张量类别，这是一个拓扑结构，在结中不变，Anyons和保形场理论中产生的拓扑结构。我对使用量子组代数的保守电流的玻尔兹曼权重得出了一个简单的约束。所得的三角重量通常是关键的集成晶格模型的权重，因此此处的方法给出了一种线性的“保障”方法，即从拓扑数据中构建Yang-Baxter方程的解决方案。这也阐明了为什么许多模型不接受解决方案。我讨论了几何和本地模型中的许多示例，包括（也许）新解决方案。
Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from "discrete holomorphicity". I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of "Baxterising", i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution.
