可积性与辫状张量范畴
Integrability and braided tensor categories
摘要：
许多可积统计力学模型都具有分数自旋守恒流。这样的电流是利用量子群代数和“离散全纯性”的思想构造的。我发现他们自然和更普遍地使用编织张量范畴，拓扑结构中产生的结不变量，任意子和共形场论。我推导出一个简单的限制玻尔兹曼权重承认一个保守的电流，概括一个发现使用量子群代数。由此产生的三角权重通常是临界可积晶格模型的三角权重，因此这里的方法给出了一种线性的“简化”方式，即从拓扑数据中构建Yang-Baxter方程的解。这也解释了为什么许多模型不承认一个解决方案。我讨论了几何和局部模型中的许多例子，包括（也许）一个新的解决方案。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
