Wild Algebras: Two Examples

TL;DR

This paper presents two specific examples of wild algebras to address gaps in understanding their behavior, contributing concrete cases to a largely unexplored area.

Contribution

It introduces two explicit examples of wild algebras that clarify questions about their properties and behaviors.

Findings

Provided the first concrete examples of wild algebras addressing open questions.

Illustrated specific behaviors of wild algebras through these examples.

Enhanced understanding of the diversity within wild algebra structures.

Abstract

Let k be a field and A a finite-dimensional k-algebra (associative, with 1). A recent preprint by Chindris, Kinser and Weyman draws the attention to the present sheer ignorance concerning the possible behavior of wild algebras. The aim of this note is to exhibit two examples which answer questions mentioned in the paper.