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Averaging t-structures and extension closure of aisles

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Averaging t-structures and extension closure of aisles. / Broomhead, Nathan; Pauksztello, David; Ploog, David.
In: Journal of Algebra, Vol. 394, 15.11.2013, p. 51-78.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Broomhead, N, Pauksztello, D & Ploog, D 2013, 'Averaging t-structures and extension closure of aisles', Journal of Algebra, vol. 394, pp. 51-78. https://doi.org/10.1016/j.jalgebra.2013.07.007

APA

Broomhead, N., Pauksztello, D., & Ploog, D. (2013). Averaging t-structures and extension closure of aisles. Journal of Algebra, 394, 51-78. https://doi.org/10.1016/j.jalgebra.2013.07.007

Vancouver

Broomhead N, Pauksztello D, Ploog D. Averaging t-structures and extension closure of aisles. Journal of Algebra. 2013 Nov 15;394:51-78. Epub 2013 Jul 31. doi: 10.1016/j.jalgebra.2013.07.007

Author

Broomhead, Nathan ; Pauksztello, David ; Ploog, David. / Averaging t-structures and extension closure of aisles. In: Journal of Algebra. 2013 ; Vol. 394. pp. 51-78.

Bibtex

@article{22d96e1fc4a4491299a78385abe9d1a2,
title = "Averaging t-structures and extension closure of aisles",
abstract = "We ask when a finite set of t-structures in a triangulated category can be {\textquoteleft}averaged{\textquoteright} 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.",
keywords = "T-structure, Aisle, Tame hereditary algebra",
author = "Nathan Broomhead and David Pauksztello and David Ploog",
year = "2013",
month = nov,
day = "15",
doi = "10.1016/j.jalgebra.2013.07.007",
language = "English",
volume = "394",
pages = "51--78",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "ELSEVIER ACADEMIC PRESS INC",

}

RIS

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.

KW - T-structure

KW - Aisle

KW - Tame hereditary algebra

U2 - 10.1016/j.jalgebra.2013.07.007

DO - 10.1016/j.jalgebra.2013.07.007

M3 - Journal article

VL - 394

SP - 51

EP - 78

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -