Representation-finite tensor product of simply connected algebras

TL;DR

This paper investigates when the tensor product of two simply connected algebras with multiple simple modules has finite representation type, providing a classification for such cases.

Contribution

It characterizes the conditions under which the tensor product of two simply connected algebras is representation-finite.

Findings

Identifies criteria for representation-finiteness of tensor products

Provides a classification for simply connected algebras with at least three simples

Advances understanding of tensor product behavior in algebra representation theory

Abstract

We determine the representation-finiteness of $A\otimes B$, where both $A$ and $B$ are simply connected algebras with at least three simple modules.