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On algebras of finite general representation type

Ryan Kinser, Danny Lara

Abstract

We introduce the notion of ``finite general representation type'' for a finite-dimensional algebra, a property related to the ``dense orbit property'' introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial, and algebraic methods to produce a family of algebras of wild representation type but finite general representation type. For completeness, we also give a short proof that the only local algebras of discrete general representation type are already of finite representation type. We end with a Brauer-Thrall style conjecture for general representations of algebras.

On algebras of finite general representation type

Abstract

We introduce the notion of ``finite general representation type'' for a finite-dimensional algebra, a property related to the ``dense orbit property'' introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial, and algebraic methods to produce a family of algebras of wild representation type but finite general representation type. For completeness, we also give a short proof that the only local algebras of discrete general representation type are already of finite representation type. We end with a Brauer-Thrall style conjecture for general representations of algebras.
Paper Structure (3 sections, 1 theorem, 2 equations)

This paper contains 3 sections, 1 theorem, 2 equations.

Table of Contents

  1. Introduction
  2. Context and motivation
  3. Main result and related literature

Key Result

Theorem 1.2

Consider the algebras $\Lambda(m,n)$ given by the following quiver with relations.

Theorems & Definitions (1)

  • Theorem 1.2