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Preprojective Algebras, Singularity Categories and Orthogonal Decompositions Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Continuous Frobenius Categories

Authors : Kiyoshi Igusa, Gordana Todorov

Published in: Algebras, Quivers and Representations

Publisher: Springer Berlin Heidelberg

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Abstract

We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are Krull-Schmidt with one indecomposable object for each pair of (not necessarily distinct) points on the circle. By putting restrictions on these points we obtain various Frobenius subcategories. The main purpose of constructing these Frobenius categories is to give a precise and elementary description of the triangulated structure of their stable categories. We show in Igusa and Todorov (arXiv:​1209.​1879, 2012) for which parameters these stable categories have cluster structure in the sense of Buan et al. (Compos. Math. 145:1035–1079, 2009) and we call these continuous cluster categories.

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previous chapter Algebras of Finite Global Dimension
next chapter Triangle Functors over Generic Hypersurfaces
Literature
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A. B. Buan, O. Iyama, I. Reiten, J. Scott, Cluster structures for 2-Calabi-Yau categories and unipotent groups, Compos. Math. 145, no. 4 (2009), 1035–1079. MathSciNetMATHCrossRef
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B. Keller, I. Reiten, Acyclic Calabi-Yau categories, with an appendix by Michel Van den Bergh, Compos. Math. 144 (2008), 1332–1348. MathSciNetMATHCrossRef
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Metadata
Title
Continuous Frobenius Categories
Authors
Kiyoshi Igusa
Gordana Todorov
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Algebras, Quivers and Representations

Print ISBN: 978-3-642-39484-3

Electronic ISBN: 978-3-642-39485-0

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-39485-0_6

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