52 research outputs found
Averaging t-structures and extension closure of aisles
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.Comment: 26 pages, 11 figures. v2: fixed minor mistakes, improved
presentation. Comments still welcome
Spherical subcategories in representation theory
We introduce a new invariant for triangulated categories: the poset of
spherical subcategories ordered by inclusion. This yields several numerical
invariants, like the cardinality and the height of the poset. We explicitly
describe spherical subcategories and their poset structure for derived
categories of certain finite-dimensional algebras.Comment: 36 pages, many changes to improve presentation, same content as
published versio
Spherical subcategories in algebraic geometry
We study objects in triangulated categories which have a two-dimensional
graded endomorphism algebra. Given such an object, we show that there is a
unique maximal triangulated subcategory, in which the object is spherical. This
general result is then applied to algebraic geometry.Comment: 21 pages. Identical to published version. There is a separate article
with examples from representation theory, see arXiv:1502.0683
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