Research ArticleOpen AccessGoogle Scholar indexed
Torsion Pairs in Triangulated Categories
College of Applied Sciences, Beijing University of Technology, Beijing, China
College of Applied Sciences, Beijing University of Technology, Beijing, China
- 1 College of Applied Sciences, Beijing University of Technology, Beijing, China
- 2 College of Applied Sciences, Beijing University of Technology, Beijing, China
Advances in Pure Mathematics·Volume 03 (2013)·Pages 374–379·Published 8 May 2013·DOI10.4236/apm.2013.33054
Copy link · social · email
Abstract
We study the properties of torsion pairs in triangulated category by introducing the notions of d-Ext-projectivity and d-Ext-injectivity. In terms of - mutation of torsion pairs, we investigate the properties of torsion pairs in triangulated category under some conditions on subcategories and in .
Keywordsd-Ext-Projectivity (d-Ext-Injectivity)Torsion PairsD-MutationTriangulated Category
- A. Beilinson, J. Bernstein and P. Deligne, “Faisceaux Pervers,” Asterisque 100, 1982.
- A. Beligiannis and I. Reiten, “Homological and Homotopical Aspects of Torsion Theories,” 2007. http://www.math.uoi.gr/~abeligia/torsion.pdf
- A. L. Gorodentsev and A. N. Rudakov, “Exceptional Vector Bundles on Projective Spaces,” Duke Mathematical Journal, Vol. 54, No. 1, 1987, pp. 115-130. doi:10.1215/S0012-7094-87-05409-3
- S. Fomin and A. Zelevinsky, “Cluster Algebras I. Foundations,” Journal of American Mathematical Society, Vol. 15, No.2, 2002, pp. 497-529. doi:10.1090/S0894-0347-01-00385-X
- S. Fomin and A. Zelevinsky, “Cluster Algebras II. Finite Type Classification,” Inventiones Mathematicae, Vol. 154, No. 1, 2003, pp. 63-121. doi:10.1007/s00222-003-0302-y
- A. Buan, R. Marsh, M. Reineke, I. Reiten and G. Todorov, “Tilting Theory and Cluster Combinations,” Advances in Mathematics, Vol. 204, No. 2, 2006, pp. 572-618. doi:10.1016/j.aim.2005.06.003
- C. Geiss, B. Leclerc and J. Schroer, “Rigid Modules over Preprojective Algebras,” Inventiones Mathematicae, Vol. 165, No. 3, 2006, pp. 589-632. doi:10.1007/s00222-006-0507-y
- M. Kontsevich, “Triangulated Categories and Geometry,” The école Normale Supérieure, Paris, 1998.
- O. Iyama and Y. Yoshino, “Mutations in Triangulated Categories and Rigid Cohen-Macaulay Modules,” Inventiones mathematicae, Vol. 172, No. 1, 2008, pp. 117-168. doi:10.1007/s00222-007-0096-4
- Y. Zhou and B. Zhu, “Mutation of Torsion Pairs in Triangulated Categories and Its Geometric Realization,” arXiv.org, Los Alamos, 2011.
- M. Auslander and S. O. Smal?, “Almost Split Sequences in Subcategories,” Journal of Algebra, Vol. 69, No. 2, 1981, pp. 426-454. doi:10.1016/0021-8693(81)90214-3
- B. Keller and I. Reiten, “Cluster-Tilted Algebras Are Gorenstein and Stably Calabi-Yau,” Advances in Mathematics, Vol. 211, No. 1, 2007, pp. 123-151. doi:10.1016/j.aim.2006.07.013
- Y. Zhou and B. Zhu, “Cluster Combinatorics of d-Cluster Categories,” Journal of Algebra, Vol. 321, No. 10, 2009, pp. 2898-2915. doi:10.1016/j.jalgebra.2009.01.032