Details
Original language | English |
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Pages (from-to) | 51-78 |
Number of pages | 28 |
Journal | Journal of Algebra |
Volume | 394 |
Early online date | 31 Jul 2013 |
Publication status | Published - 15 Nov 2013 |
Abstract
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In: Journal of Algebra, Vol. 394, 15.11.2013, p. 51-78.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Averaging t-structures and extension closure of aisles
AU - Broomhead, Nathan
AU - Pauksztello, David
AU - Ploog, David
PY - 2013/11/15
Y1 - 2013/11/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84881226223&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1208.5691
DO - 10.48550/arXiv.1208.5691
M3 - Article
AN - SCOPUS:84881226223
VL - 394
SP - 51
EP - 78
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -