论文标题
$ g $ - 杂交的编织装饰
$G$-crossed braided zesting
论文作者
论文摘要
对于有限的组$ g $，$ g $的编织融合类别是$ g $ raded的融合类别，具有其他结构，即$ g $ - action和$ g $ baiding。我们开发了$ g $ - 加入的编织式Zesting：一种明确的方法，用于从给定的$ g $ $ g $ od-g $ o的编织融合类别中通过类别和分级组$ g $相关的共同体学数据来构建新的编织融合类别。这是通过对作者最近描述的（编织）融合类别的类似结构进行调整来实现的。给定类别$ \ MATHCAL {C} $的所有$ G $ - 涂布的编织式均为$ g $ - 延伸其琐碎的组件，并且可以根据基于同质的Etingof，Nikshych和Ostrik的同质描述来解释。特别是，我们明确描述了哪些$ g $延误对应于$ g $涂的编织式Zestings。
For a finite group $G$, a $G$-crossed braided fusion category is $G$-graded fusion category with additional structures, namely a $G$-action and a $G$-braiding. We develop the notion of $G$-crossed braided zesting: an explicit method for constructing new $G$-crossed braided fusion categories from a given one by means of cohomological data associated with the invertible objects in the category and grading group $G$. This is achieved by adapting a similar construction for (braided) fusion categories recently described by the authors. All $G$-crossed braided zestings of a given category $\mathcal{C}$ are $G$-extensions of their trivial component and can be interpreted in terms of the homotopy-based description of Etingof, Nikshych and Ostrik. In particular, we explicitly describe which $G$-extensions correspond to $G$-crossed braided zestings.
