论文标题
稳定模块类别的分类动力学
Categorical dynamics on stable module categories
论文作者
论文摘要
让$ a $成为有限的连接分级的共同共同霍夫夫代数在$ k $上。稳定的模块类别$ \ mathrm {stmod} _a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ $ \ mathsf {tw} $，$ 1 $ 1 $。我们显示$ \ mathsf {tw} $的分类熵为零。我们为$ a $ a $的共同体的krull尺寸和$ \ mathsf {tw} $的分类多项式熵提供了一个下限，并且就特定形式的$ a $ a-Modules的有限分辨率而言，上限。我们使用这些工具来计算Twist Foundor的分类多项式熵，以在$ \ Mathbb {f} _2 $上进行有限分级的Hopf代数示例。
Let $ A $ be a finite connected graded cocommutative Hopf algebra over a field $ k $. There is an endofunctor $ \mathsf{tw} $ on the stable module category $ \mathrm{StMod}_A $ of $ A $ which twists the grading by $ 1 $. We show the categorical entropy of $ \mathsf{tw} $ is zero. We provide a lower bound for the categorical polynomial entropy of $ \mathsf{tw} $ in terms of the Krull dimension of the cohomology of $ A $, and an upper bound in terms of the existence of finite resolutions of $ A $-modules of a particular form. We employ these tools to compute the categorical polynomial entropy of the twist functor for examples of finite graded Hopf algebras over $ \mathbb{F}_2 $.
