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Sparseness of t-structures and negative Calabi-Yau dimension in triangulated categories generated by a spherical object

Lookup NU author(s): Professor Peter Jorgensen

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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 Σ^w is the unique power of the suspension functor which is a Serre functor.

Publication metadata

Author(s): Holm T, Jorgensen P, Yang D

Publication type: Article

Publication status: Published

Journal: Bulletin of the London Mathematical Society

Year: 2013

Volume: 45

Issue: 1

Pages: 120-130

Print publication date: 30/09/2012

ISSN (print): 0024-6093

ISSN (electronic): 1469-2120

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1112/blms/bds072

DOI: 10.1112/blms/bds072

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