Details
| Original language | English |
|---|---|
| Pages (from-to) | 120-130 |
| Number of pages | 11 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 45 |
| Issue number | 1 |
| Publication status | Published - Feb 2013 |
Abstract
Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classic. For instance, if w = 0, then it is the compact derived category of the dual numbers over k. Our main results are that, for w ≤ 0, the category T has no non-trivial t-structures, but does have one family of non-trivial co-t-structures, whereas, for w ≥ 1, the opposite statement holds. Moreover, without any claim to originality, we observe that for w ≤ -1, the category T is a candidate to have negative Calabi-Yau dimension since Σw is the unique power of the suspension functor which is a Serre functor.
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In: Bulletin of the London Mathematical Society, Vol. 45, No. 1, 02.2013, p. 120-130.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Sparseness of t-structures and negative Calabi-Yau dimension in triangulated categories generated by a spherical object
AU - Holm, Thorsten
AU - Jorgensen, Peter
AU - Yang, Dong
N1 - Funding Information: Thorsten Holm and Peter Jørgensen were supported by the research priority programme SPP 1388 Darstellungstheorie of the Deutsche Forschungsgemeinschaft (DFG). They gratefully acknowledge the financial support through the grant HO 1880/4-1.
PY - 2013/2
Y1 - 2013/2
N2 - Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classic. For instance, if w = 0, then it is the compact derived category of the dual numbers over k. Our main results are that, for w ≤ 0, the category T has no non-trivial t-structures, but does have one family of non-trivial co-t-structures, whereas, for w ≥ 1, the opposite statement holds. Moreover, without any claim to originality, we observe that for w ≤ -1, the category T is a candidate to have negative Calabi-Yau dimension since Σw is the unique power of the suspension functor which is a Serre functor.
AB - Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classic. For instance, if w = 0, then it is the compact derived category of the dual numbers over k. Our main results are that, for w ≤ 0, the category T has no non-trivial t-structures, but does have one family of non-trivial co-t-structures, whereas, for w ≥ 1, the opposite statement holds. Moreover, without any claim to originality, we observe that for w ≤ -1, the category T is a candidate to have negative Calabi-Yau dimension since Σw is the unique power of the suspension functor which is a Serre functor.
UR - http://www.scopus.com/inward/record.url?scp=84876552210&partnerID=8YFLogxK
U2 - 10.1112/blms/bds072
DO - 10.1112/blms/bds072
M3 - Article
AN - SCOPUS:84876552210
VL - 45
SP - 120
EP - 130
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 1
ER -