Modules of constant Jordan type

Jon F. Carlson; Eric M. Friedlander; Julia Pevtsova

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arXiv · 0707.3845

Modules of constant Jordan type

Jon F. Carlson·Eric M. Friedlander·Julia Pevtsova

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Abstract

We introduce the class of modules of constant Jordan type for a finite group scheme $G$ over a field $k$ of characteristic $p > 0$. This class is closed under taking direct sums, tensor products, duals, Heller shifts and direct summands, and includes endotrivial modules. It contains all modules in an Auslander-Reiten component which has at least one module in the class. Highly non-trivial examples are constructed using cohomological techniques. We offer conjectures suggesting that there are strong conditions on a partition to be the Jordan type associated to a module of constant Jordan type.

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Jon F. Carlson, Eric M. Friedlander, Julia Pevtsova. 2007-07-25. Modules of constant Jordan type. https://arxiv.org/abs/0707.3845

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