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

## 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 (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.