The derived-discrete algebras over the real numbers

TL;DR

This paper classifies derived-discrete algebras over the real numbers by extending the known complex case, using quiver presentations and Morita equivalence to understand their structure.

Contribution

It provides a classification of real derived-discrete algebras up to Morita equivalence, building on complex classifications and analyzing their quiver presentations.

Findings

Complete classification of real derived-discrete algebras.

Extension of complex classification results to real algebras.

Use of quiver presentations to analyze algebra structures.

Abstract

We classify derived-discrete algebras over the real numbers up to Morita equivalence, using the classification of complex derived-discrete algebras in [{\sc D. Vossieck}, {\em The algebras with discrete derived category}, J. Algebra {\bf 243} (2001), 168--176]. To this end, we investigate the quiver presentation of the complexified algebra of a real algebra given by a modulated quiver and an admissible ideal.