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arXiv 1702.08475math.QAmath.CT
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Hom-张量范畴与Hom-杨-巴克斯特方程

Hom-Tensor Categories and the Hom-Yang-Baxter Equation

Florin Panaite, Paul Schrader, Mihai D. Staic

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36 pages, many diagrams
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摘要：

我们引入了一种新的类型的范畴对象称为\emph{hom-tensor category}，并表明它提供了适当的设置模块在任意的hom-bialgebra。接下来我们引入了\emph{hom-braided category}的概念，并证明了这是拟三角hom-bialgebra上模的正确设置。我们还证明了hom-杨-巴克斯特方程如何适合于这个框架，以及如何将具有双射结构映射的hom-bialgebra上的Yetter-Drinfeld模范畴组织成hom-braided范畴。最后证明了在一定条件下，可以从一个hom-tensor范畴（一个hom-braided范畴）得到一个张量范畴（一个braided张量范畴）。

英文摘要：

We introduce a new type of categorical object called a \emph{hom-tensor category} and show that it provides the appropriate setting for modules over an arbitrary hom-bialgebra. Next we introduce the notion of \emph{hom-braided category} and show that this is the right setting for modules over quasitriangular hom-bialgebras. We also show how the hom-Yang-Baxter equation fits into this framework and how the category of Yetter-Drinfeld modules over a hom-bialgebra with bijective structure map can be organized as a hom-braided category. Finally we prove that, under certain conditions, one can obtain a tensor category (respectively a braided tensor category) from a hom-tensor category (respectively a hom-braided category).

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