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AUSLANDER GENERATORS AND HOMOLOGICAL CONJECTURES

Published online by Cambridge University Press:  30 August 2013

JIAQUN WEI
JIAQUN WEI*
Affiliation:
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P. R. China e-mail: weijiaqun@njnu.edu.cn
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Abstract

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Let A be an artin algebra with representation dimension not more than 3. Assuming that AV is an Auslander generator and M ∈ addAV, we show that both findim(EndAM) and findim(EndAM)op are finite, and consequently the Gorenstein symmetry conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for EndAM.

Keywords

16E0516E1016G10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 3 , September 2014 , pp. 503 - 506
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Happel, D., Homological conjectures in representation theory of finite-dimensional algebras, Sherbrook Lecture Notes Series (Universit⋅e de Sherbrooke, 1991). Available at http://www.mathematik.uni-bielefeld.de/~sek/dim2/happel2.pdf, accessed 22 July 2013.Google Scholar
2.Hu, W. and Xi, C., Auslander-reiten sequences and global dimensions, Math. Res. Lett. 13 (6) (2006), 885–895.CrossRefGoogle Scholar
3.Igusa, K. and Todorov, G., On the finitistic global dimension conjecture for artin algebras, in: Representations of algebras and related topics (Fields Inst. Commun. 45, American Mathematical Society, Providence, RI, 2005), 201–204.Google Scholar
4.Mantese, F. and Reiten, I., Wakamatsu tilting modules, J. Algebra 278 (2004), 532–552.Google Scholar
5.Ringel, C. M., On the representation dimension of artin algebras, Bull. Inst Math. Acad. Sin. 7 (1) (2012), 33–70.Google Scholar
6.Zhang, A. and Zhang, S., On the finitistic dimension conjecture of artin algebras, J. Algebra 320 (1) (2008), 253–258.Google Scholar