Averaging t-structures and extension closure of aisles

Nathan Broomhead; David Pauksztello; David Ploog

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arXiv · 1208.5691

Averaging t-structures and extension closure of aisles

Nathan Broomhead·David Pauksztello·David Ploog

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Abstract

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 finite 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.

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BibTeX RIS

Nathan Broomhead, David Pauksztello, David Ploog. 2012-09-21. Averaging t-structures and extension closure of aisles. https://arxiv.org/abs/1208.5691

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