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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Zheng, Yuefei and Huang, Zhaoyong 2016. Auslander–Reiten Triangles in Homotopy Categories. Communications in Algebra, Vol. 44, Issue. 11, p. 4995.


    YANG, GANG 2015. ALMOST SPLIT SEQUENCES FOR COMPLEXES VIA RELATIVE HOMOLOGY. Journal of the Korean Mathematical Society, Vol. 52, Issue. 5, p. 1051.


    Liu, Shiping Ng, Puiman and Paquette, Charles 2013. Almost Split Sequences and Approximations. Algebras and Representation Theory, Vol. 16, Issue. 6, p. 1809.


    Ng, Puiman 2011. Existence of Auslander–Reiten sequences in subcategories. Journal of Pure and Applied Algebra, Vol. 215, Issue. 10, p. 2378.


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Auslander-Reiten triangles in subcategories

  • Peter Jørgensen (a1)
  • DOI: http://dx.doi.org/10.1017/is008007021jkt056
  • Published online: 14 November 2008
Abstract
Abstract

This paper studies Auslander-Reiten triangles in subcategories of triangulated categories. The main theorem shows that the Auslander-Reiten triangles in a subcategory are closely connected with the approximation properties of the subcategory. Namely, let C be an object in the subcategory C of the triangulated category T, and let

be an Auslander-Reiten triangle in T. Then under suitable assumptions, there is an Auslander-Reiten triangle

in C if and only if there is a minimal right-C-approximation of the form

.

The theory is used to give a new proof of the existence of Auslander-Reiten sequences over finite dimensional algebras.

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15.C. M. Ringel , “Tame algebras and quadratic forms”, Lecture Notes in Math. 1099, Springer, Berlin, 1984

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Journal of K-Theory
  • ISSN: 1865-2433
  • EISSN: 1865-5394
  • URL: /core/journals/journal-of-k-theory
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