The Representation Type of the Descent Algebras of Type \mathbbA

2024/07/09 by Karin Erdmann, Kay Jin Lim, Erdmann, Karin +1
Computer Science · Mathematics · #05E10 #20C30 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2407.06471

openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the representation type of the descent algebras of type \A in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method relies on a surjective algebra homomorphism from a descent algebra of type \A to another of lower degree. For small degree cases, we employ techniques from the representation theory of finite-dimensional algebras.

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