On the graded dual numbers, arcs, and non-crossing partitions of the integers

Gratz, S. and Stevenson, G. (2018) On the graded dual numbers, arcs, and non-crossing partitions of the integers. Journal of Algebra, 515, pp. 360-388. (doi:10.1016/j.jalgebra.2018.08.023)

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Abstract

We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this model we describe the lattice of thick subcategories of the bounded derived category, and of the perfect complexes, in terms of non-crossing partitions. We also make some comments on the symmetries of these lattices, exceptional collections, and the analogous problem for the unbounded derived category.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Stevenson, Dr Gregory and Gratz, Dr Sira
Authors: Gratz, S., and Stevenson, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra
Publisher:Elsevier
ISSN:0021-8693
ISSN (Online):1090-266X
Published Online:07 September 2018
Copyright Holders:Copyright © 2018 Elsevier Inc.
First Published:First published in Journal of Algebra 515: 360-388
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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