Grabowski, JE and Pressland, M orcid.org/0000-0002-9631-3583 (2018) Graded Frobenius cluster categories. Documenta Mathematica, 23. pp. 49-76. ISSN 1431-0635
Abstract
Recently the first author studied multi-gradings for generalised cluster categories, these being 2-Calabi-Yau triangulated categories with a choice of cluster-tilting object. The grading on the category corresponds to a grading on the cluster algebra without coefficients categorified by the cluster category and hence knowledge of one of these structures can help us study the other. In this work, we extend the above to certain Frobenius categories that categorify cluster algebras with coefficients. We interpret the grading K-theoretically and prove similar results to the triangulated case, in particular obtaining that degrees are additive on exact sequences. We show that the categories of Buan, Iyama, Reiten and Scott, some of which were used by Geiß, Leclerc and Schröer to categorify cells in partial flag varieties, and those of Jensen, King and Su, categorifying Grassmannians, are examples of graded Frobenius cluster categories.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 FIZ Karlsruhe GmbH. This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | cluster algebra, Frobenius category, grading, Grothendieck group |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Apr 2020 11:42 |
Last Modified: | 03 Apr 2020 11:42 |
Status: | Published |
Identification Number: | 10.25537/dm.2018v23.49-76 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:159076 |