Hostname: page-component-6bf8c574d5-qdpjg Total loading time: 0 Render date: 2025-02-21T05:27:13.429Z Has data issue: false hasContentIssue false
  • English
  • Français

Quotients of cluster categories

Published online by Cambridge University Press:  04 February 2010

Peter Jørgensen
Peter Jørgensen
Affiliation:
School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK, (peter.jorgensen@ncl.ac.uk)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Higher cluster categories were recently introduced as a generalization of cluster categories. This paper shows that in Dynkin types A and D, half of all higher cluster categories can be obtained as quotients of cluster categories. The other half are quotients of 2-cluster categories, the ‘lowest’ type of higher cluster categories. Hence, in Dynkin types A and D, all higher cluster phenomena are implicit in cluster categories and 2-cluster categories. In contrast, the same is not true in Dynkin type E.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 65 - 81
Copyright
Copyright © Royal Society of Edinburgh 2010