Averaging t-structures and extension closure of aisles

Broomhead, Nathan and Pauksztello, David and Ploog, David (2013) Averaging t-structures and extension closure of aisles. Journal of Algebra, 394. pp. 51-78. ISSN 0021-8693

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We ask when a finite set of t-structures in a triangulated category can be ‘averaged’ into one t-structure or, equivalently, when the extension closure of a finite set of aisles is again an aisle. There is a straightforward, positive answer for a (possibly infinite) set of compactly generated t-structures in a big triangulated category. For piecewise tame hereditary categories, we give a criterion for when averaging is possible, and an algorithm that computes truncation triangles in this case. A finite group action on a triangulated category gives a natural way of producing a finite set of t-structures out of a given one. If averaging is possible, there is an induced t-structure on the equivariant triangulated category.

Item Type: Journal Article
Journal or Publication Title: Journal of Algebra
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2602
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 88020
Deposited By: ep_importer_pure
Deposited On: 06 Oct 2017 19:38
Refereed?: Yes
Published?: Published
Last Modified: 01 Jan 2020 10:28
URI: https://eprints.lancs.ac.uk/id/eprint/88020

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