Publication: Categorical dynamics on stable module categories
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2023-05-16
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Yang, Lucy. 2023. Categorical dynamics on stable module categories. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.
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Abstract
Let A be a finite connected graded cocommutative Hopf algebra over a field k. There is an
endofunctor tw on the stable module category StMod A of A which twists the grading by 1.
We show the categorical entropy of tw is zero. We provide a lower bound for the categorical
polynomial entropy of 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 F 2 .
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