Modules of constant Jordan type

2007/07/25 by Jon Carlson, Carlson, Jon F., Eric M. Friedlander +3 · 2 citations
Decision Sciences · Mathematics · #16G10 (primary) #20C20 #20G10 (secondary) #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fuzzy and Soft Set Theory #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0707.3845

openalex publication_date 2007/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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