Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-25T21:21:09.248Z Has data issue: false hasContentIssue false
  • English
  • Français

On the centre of a triangulated category

Part of: Abelian categories Homological methods

Published online by Cambridge University Press:  07 April 2011

Henning Krause  and
Yu Ye
Henning Krause
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany (hkrause@math.uni-bielefeld.de)
Yu Ye
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, People's Republic of China (yeyu@ustc.edu.cn)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We discuss some basic properties of the graded centre of a triangulated category and compute examples arising in representation theory of finite-dimensional algebras.

Keywords

triangulated categoryderived categorygraded centre

MSC classification

Secondary: 18E30: Derived categories, triangulated categories 16E35: Derived categories
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 443 - 466
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Amdal, I. K. and Ringdal, F., Catégories unisérielles, C. R. Acad. Sci. Paris Sér. A 267 (1968), 85–87.Google Scholar
2.Arnold, D. M. and Laubenbacher, R. C., Almost split sequences for Dedekind-like rings, J. Lond. Math. Soc. (2) 43 (1991), 225–235.CrossRefGoogle Scholar
3.Avramov, L. L. and Iyengar, S. B., Constructing modules with prescribed cohomological support, Illinois J. Math. 51(1) (2007), 1–20.CrossRefGoogle Scholar
4.Benson, D., Iyengar, S. B. and Krause, H., Local cohomology and support for triangulated categories, Annales Scient. Éc. Norm. Sup. 4 (2008), 573–619.Google Scholar
5.Buchweitz, R.-O. and Flenner, H., Global Hochschild (co-)homology of singular spaces, Adv. Math. 217 (2008), 205–242.CrossRefGoogle Scholar
6.Cuadra, J. and Gómez-Torrecillas, J., Serial coalgebras, J. Pure Appl. Alg. 189 (2004), 89–107.CrossRefGoogle Scholar
7.Geigle, W. and Lenzing, H., A class of weighted projective lines arising in representation theory of finite dimensional algebras, in Singularities, representation of algebras, and vector bundles, Lecture Notes in Mathematics, Volume 1273, pp. 265–297 (Springer, 1987).CrossRefGoogle Scholar
8.Happel, D., A characterization of hereditary categories with tilting object, Invent. Math. 144 (2001), 381–398.CrossRefGoogle Scholar
9.Kessar, R. and Linckelmann, M., The graded center of the stable category of a Brauer tree algebra, Q. J. Math. 61 (2010), 337–349.CrossRefGoogle Scholar
10.Krause, H., Derived categories, resolutions and Brown representability, in Interactions between homotopy theory and algebra, Contemporary Mathematics, Volume 436, pp. 101–139 (American Mathematical Society, Providence, RI, 2007).CrossRefGoogle Scholar
11.Künzer, M., On the center of the derived category, Preprint (2006).Google Scholar
12.Lenzing, H., Hereditary categories, in Handbook of tilting theory, pp. 105–146 (Cambridge University Press, 2007).CrossRefGoogle Scholar
13.Linckelmann, M., On graded centers and block cohomology, Proc. Edinb. Math. Soc. 52 (2009), 489–514.CrossRefGoogle Scholar
14.Lowen, W. and van den Bergh, M., Hochschild cohomology of abelian categories and ringed spaces, Adv. Math. 198 (2005), 172–221.CrossRefGoogle Scholar
15.Rouquier, R., Representation dimension of exterior algebras, Invent. Math. 165 (2006), 357–367.CrossRefGoogle Scholar
16.Simson, D., On coalgebras of tame comodule type, in Representations of algebra, Volume II, pp. 450–486 (Beijing Normal University Press, 2002).Google Scholar