The Chromatic Brauer Category and Its Linear Representations
The Chromatic Brauer Category and Its Linear Representations
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半音布劳尔范畴及其线性表示
DOI：
10.1007/s10485-020-09619-5
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发表时间：
2020
影响因子：
0.6
通讯作者：
Wrazidlo Dominik J.
中科院分区：
文献类型：
--
作者：
Mueller L. Felipe;Wrazidlo Dominik J.
Brauer范畴是一个对称的严格monoidal范畴，它是在Banagl的正拓扑场论（英语：Positive topological field theories，TFT）框架下Brauer代数的（水平）范畴化。我们引入色Brauer范畴作为Brauer范畴的丰富，其中态射是分量标记的。（色）布劳尔范畴的线性表示是对称的严格monoidal函子到真实的向量空间和配备Schauenburg张量积的线性映射的范畴中。本文研究了（色）Brauer范畴的表示理论，并对它的所有忠实线性表示进行了分类。作为一个应用，我们使用折叠线的指数来构造Banagl的基于折叠映射到平面上的具体正TFT的精化。
The Brauer category is a symmetric strict monoidal category that arises as a (horizontal) categorification of the Brauer algebras in the context of Banagl’s framework of positive topological field theories (TFTs). We introduce the chromatic Brauer category as an enrichment of the Brauer category in which the morphisms are component-wise labeled. Linear representations of the (chromatic) Brauer category are symmetric strict monoidal functors into the category of real vector spaces and linear maps equipped with the Schauenburg tensor product. We study representation theory of the (chromatic) Brauer category, and classify all its faithful linear representations. As an application, we use indices of fold lines to construct a refinement of Banagl’s concrete positive TFT based on fold maps into the plane.