AN INDUCTIVE MACHINERY FOR REPRESENTATIONS OF CATEGORIES WITH SHIFT FUNCTORS

作者：Gan, Wee Liang^*; Li, Liping

来源：Transactions of the American Mathematical Society, 2019, 371(12): 8513-8534.

DOI：10.1090/tran/7554

• FI-MODULES
• STABILITY
• HOMOLOGY

We describe an inductive machinery to prove various properties of representations of a category equipped with a generic shift functor. Specifically, we show that if a property (P) of representations of the category behaves well under the generic shift functor, then all finitely generated representations of the category have the property (P). In this way, we obtain simple criteria for properties such as Noetherianity, finiteness of Castelnuovo-Mumford regularity, and polynomial growth of dimension to hold. This gives a systemetic and uniform proof of such properties for representations of the categories FIG and OIG which appear in representation stability theory.

• 出版日期2019-6-15
• 单位湖南师范大学