论文标题
ISING模块化类别中的fibonacci型Orbifold数据
Fibonacci-type orbifold data in Ising modular categories
论文作者
论文摘要
Orbifold基准是一个集合$ \ Mathbb {a} $在模块化融合类别中的代数数据$ \ Mathcal {C} $。它允许一个人在建筑中定义新的模块化融合类别$ \ mathcal {c} _ {\ mathbb {a}} $，该结构是将融合类别的德林菲尔德中心的概括。在某些简化的假设下，我们表征Orbifold数据$ \ Mathbb {a} $在满足多项式方程的标量方面，并给出明确的表达式，该表达式计算了$ \ Mathcal {C} _ {c} _ {\ MathBb {\ Mathbb {a}} $的简单对象的数字数量。 在Ising型模块化类别中，我们找到了Orbifold数据的新示例，从适当的意义上讲，这些数据显示了fibonacci融合规则。相应的Orbifold模块化类别具有11个简单对象，对于某个参数选择，可以在10级的$ sl（2）$中获得模块化类别。此构造将$ e_6 $交换性代数的后一种类别颠倒。
An orbifold datum is a collection $\mathbb{A}$ of algebraic data in a modular fusion category $\mathcal{C}$. It allows one to define a new modular fusion category $\mathcal{C}_{\mathbb{A}}$ in a construction that is a generalisation of taking the Drinfeld centre of a fusion category. Under certain simplifying assumptions we characterise orbifold data $\mathbb{A}$ in terms of scalars satisfying polynomial equations and give an explicit expression which computes the number of isomorphism classes of simple objects in $\mathcal{C}_{\mathbb{A}}$. In Ising-type modular categories we find new examples of orbifold data which - in an appropriate sense - exhibit Fibonacci fusion rules. The corresponding orbifold modular categories have 11 simple objects, and for a certain choice of parameters one obtains the modular category for $sl(2)$ at level 10. This construction inverts the extension of the latter category by the $E_6$ commutative algebra.
