Continuous Quivers of Type A (III) Embeddings of Cluster Theories
Abstract
We continue the work started in parts (I) and (II). In this part we classify which continuous type A quivers are derived equivalent and introduce the new continuous cluster category with E-clusters, which are a generalization of clusters. In the middle we provide a rigorous connection between the previous construction of the continuous cluster category and the new construction. We conclude with the introduction of a cluster theory, generalizing the notion of a cluster structure. Using this new notion, we demonstrate how one embeds known type A cluster theories into the new E-cluster theory in a way compatible with mutation. This is part (III) in a series of work that will conclude with a continuous generalization of mutation for cluster theories.
Cite
@article{arxiv.2004.10740,
title = {Continuous Quivers of Type A (III) Embeddings of Cluster Theories},
author = {Kiyoshi Igusa and Job D. Rock and Gordana Todorov},
journal= {arXiv preprint arXiv:2004.10740},
year = {2025}
}
Comments
37 pages. This is the version before the accepted version, per journal requirement