The Representation Type of the Descent Algebras of Type $\mathbb{A}$
Karin Erdmann, Kay Jin Lim

TL;DR
This paper classifies when descent algebras of type A have finite or wild representation types, showing they are mostly wild except for small degrees, using algebra homomorphisms and representation theory techniques.
Contribution
It provides a complete classification of the representation type of type A descent algebras in positive characteristic, highlighting the finite cases and the general wild behavior.
Findings
Finite representation type only for small degrees
Most descent algebras are wild in larger degrees
Uses algebra homomorphisms and finite-dimensional algebra techniques
Abstract
We classify the representation type of the descent algebras of type 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 to another of lower degree. For small degree cases, we employ techniques from the representation theory of finite-dimensional algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra · Rings, Modules, and Algebras
