Auslander's defect formula and a commutative triangle in an exact category

Pengjie JIAO

PDF(252 KB)
PDF(252 KB)
Front. Math. China ›› 2020, Vol. 15 ›› Issue (1) : 115-125. DOI: 10.1007/s11464-020-0814-4
RESEARCH ARTICLE
RESEARCH ARTICLE

Auslander's defect formula and a commutative triangle in an exact category

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Abstract

We prove Auslander's defect formula in an exact category, and obtain a commutative triangle involving the Auslander bijections and the generalized Auslander{Reiten duality.

Keywords

Auslander's defect formula / Auslander bijections / morphisms determined by objects

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Pengjie JIAO. Auslander's defect formula and a commutative triangle in an exact category. Front. Math. China, 2020, 15(1): 115‒125 https://doi.org/10.1007/s11464-020-0814-4

References

[1]
Auslander M. Functors and morphisms determined by objects. In: Gordon R, ed. Representation Theory of Algebras: Proceedings of the Philadelphia Conference. Lecture Notes in Pure and Applied Mathematics, Vol 37. New York: Marcel Dekker, 1978, 1–244
[2]
Auslander M, Reiten I, Smal S O. Representation Theory of Artin Algebras. Cambridge Stud Adv Math, Vol 36. Cambridge: Cambridge Univ Press, 1995
CrossRef Google scholar
[3]
Chen X W. The Auslander bijections and universal extensions. Ark Mat, 2017, 55: 41–59
CrossRef Google scholar
[4]
Iyama O. Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories. Adv Math, 2007, 210: 22–50
CrossRef Google scholar
[5]
Jasso G, Kvamme S. An introduction to higher Auslander-Reiten theory. Bull Lond Math Soc, 2019, 51: 1–24
CrossRef Google scholar
[6]
Jiao P. The generalized Auslander-Reiten duality on an exact category. J Algebra Appl, 2018, 17: 1850227
CrossRef Google scholar
[7]
Jiao P, Le J. The Auslander-Reiten duality via morphisms determined by objects. J Pure Appl Algebra, 2018, 222: 807–817
CrossRef Google scholar
[8]
Keller B. Chain complexes and stable categories. Manuscripta Math, 1990, 67: 379–417
CrossRef Google scholar
[9]
Krause H. A short proof for Auslander's defect formula. Linear Algebra Appl, 2003, 365: 267–270
CrossRef Google scholar
[10]
Lenzing H, Zuazua R. Auslander-Reiten duality for abelian categories. Bol Soc Mat Mex (3), 2004, 10: 169–177
[11]
Ringel C M. Morphisms determined by objects: the case of modules over Artin algebras. Illinois J Math, 2012, 56: 981–1000
CrossRef Google scholar
[12]
Ringel C M. The Auslander bijections: how morphisms are determined by modules. Bull Math Sci, 2013, 3: 409–484
CrossRef Google scholar

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