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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The first author is supported by NSA Grant 98230-13-1-0247.
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Dedicated to the memory of Dieter Happel.
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Igusa, K., Todorov, G. (2013). Continuous Frobenius Categories. In: Buan, A., Reiten, I., Solberg, Ø. (eds) Algebras, Quivers and Representations. Abel Symposia, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39485-0_6
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DOI: https://doi.org/10.1007/978-3-642-39485-0_6
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