Arkiv för Matematik

Volume 55 (2017)

Number 1

The Auslander bijections and universal extensions

Pages: 41 – 59

DOI: https://dx.doi.org/10.4310/ARKIV.2017.v55.n1.a2

Author

Xiao-Wu Chen (Key Laboratory of Wu Wen-Tsun, Mathematics, Chinese Academy of Sciences, Beijing, China; and School of Mathematical Sciences, University of Science and Technology of China, Anhui, China)

Abstract

Universal extensions arise naturally in the Auslander bijections. For an abelian category having Auslander–Reiten duality, we exploit a bijection triangle, which involves the Auslander bijections, universal extensions and the Auslander–Reiten duality. Some consequences are given, in particular, a conjecture by Ringel is verified.

Keywords

universal extension, determined morphism, Auslander-Reiten duality, Auslander bijection

2010 Mathematics Subject Classification

13D07, 16G10, 16G70

Full Text (PDF format)

This work is supported by National Natural Science Foundation of China (Nos. 11522113 and 11671245), and the Fundamental Research Funds for the Central Universities.

Received 17 March 2016

Received revised 11 January 2017

Accepted 7 February 2017

Published 26 September 2017