dc.identifier.uri |
http://dx.doi.org/10.15488/2317 |
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dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/2343 |
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dc.contributor.author |
Holm, Thorsten
|
|
dc.contributor.author |
Jørgensen, Peter
|
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dc.date.accessioned |
2017-11-17T09:26:06Z |
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dc.date.available |
2017-11-17T09:26:06Z |
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dc.date.issued |
2015 |
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dc.identifier.citation |
Holm, T.; Jørgensen, P.: Generalized friezes and a modified Caldero-Chapoton map depending on a rigid object. In: Nagoya Mathematical Journal 218 (2015), Nr. 1, S. 101-124. DOI: https://doi.org/10.1215/00277630-2891495 |
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dc.description.abstract |
The (usual) Caldero-Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps reachable indecomposable objects to the corresponding cluster variables in a cluster algebra. This formalizes the idea that the cluster category is a categorification of the cluster algebra. The definition of the Caldero-Chapoton map requires the category to be 2-Calabi-Yau, and the map depends on a cluster-tilting object in the category. We study a modified version of the Caldero-Chapoton map which requires only that the category have a Serre functor and depends only on a rigid object in the category. It is well known that the usual Caldero-Chapoton map gives rise to so-called friezes, for instance, Conway-Coxeter friezes. We show that the modified Caldero-Chapoton map gives rise to what we call generalized friezes and that, for cluster categories of Dynkin type A, it recovers the generalized friezes introduced by combinatorial means in recent work by the authors and Bessenrodt. © 2015 by The Editorial Board of the Nagoya Mathematical Journal. |
eng |
dc.language.iso |
eng |
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dc.publisher |
Cambridge : Cambridge University Press |
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dc.relation.ispartofseries |
Nagoya Mathematical Journal 218 (2015), Nr. 1 |
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dc.rights |
Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
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dc.subject |
Primary 05E10 |
eng |
dc.subject |
Secondary 13F60 |
eng |
dc.subject |
16G70 |
eng |
dc.subject |
18E30 |
eng |
dc.subject.ddc |
510 | Mathematik
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ger |
dc.title |
Generalized friezes and a modified Caldero-Chapoton map depending on a rigid object |
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dc.type |
Article |
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dc.type |
Text |
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dc.relation.issn |
0027-7630 |
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dc.relation.doi |
https://doi.org/10.1215/00277630-2891495 |
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dc.bibliographicCitation.issue |
1 |
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dc.bibliographicCitation.volume |
218 |
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dc.bibliographicCitation.firstPage |
101 |
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dc.bibliographicCitation.lastPage |
124 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
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