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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, ([email protected])
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Abstract

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

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