Browse > Article
http://dx.doi.org/10.4134/CKMS.c180226

THE U-PROJECTIVE RESOLUTION OF MODULES OVER PATH ALGEBRAS OF TYPES An AND Ãn  

Baur, Karin (Institut fur Mathematik und Wissenschaftliches Rechnen Universitat Graz)
Mahatma, Yudi (Bandung Institute of Technology)
Muchtadi-Alamsyah, Intan (Bandung Institute of Technology)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.3, 2019 , pp. 701-718 More about this Journal
Abstract
In this paper we compute the U-projective resolution of kQ-modules where Q is quiver of type $A_n$ and ${\tilde{A}}_n$. The behavior of the sequence can be seen through its geometric representation.
Keywords
projective resolution; module; path algebra; quiver;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. Davvaz and Y. A. Parnian-Garamaleky, A note on exact sequences, Bull. Malaysian Math. Soc. (2) 22 (1999), no. 1, 53-56.
2 B. Davvaz and H. Shabani-Solt, A generalization of homological algebra, J. Korean Math. Soc. 39 (2002), no. 6, 881-898. https://doi.org/10.4134/JKMS.2002.39.6.881   DOI
3 Faisal, Irawati, and I. Muchtadi-Alamsyah, Auslander Reiten quiver of Nakayama algebra type Dynkin graph $A_n$, J. Math. Fundam. Sci. 45A (2013), no. 1, 1-16. https://doi.org/10.5614/j.math.fund.sci.2013.45.1.1
4 Y. Mahatma and I. Muchtadi-Alamsyah, Construction of U-extension module, AIP Conference Proceedings 1867, 2017.
5 J. J. Rotman, An Introduction to Homological Algebra, second edition, Universitext, Springer, New York, 2009. https://doi.org/10.1007/b98977
6 R. Schiffer, Quiver Representations, CMS Books in Mathematics/Ouvrages de Math-ematiques de la SMC, Springer, Cham, 2014. https://doi.org/10.1007/978-3-319-09204-1
7 M. Warkentin, Fadenmoduln uber A und cluster-kombinatorik (String modules over A and cluster-combinatorics), Diploma thesis, University of Bonn (December 2008) available from http://www.qucosa.de/fileadmin/data/qucosa/documents/9479/Diplo-marbeitMatthias Warkentin.pdf
8 K. Baur and H. A. Torkildsen, A geometric realization of tame categories, arXiv:1502.06489v1 [math.RT] 23 Feb 2015.
9 I. Assem, D. Simson, and A. Skowronski, Elements of the representation theory of associative algebras. Vol. 1, London Mathematical Society Student Texts, 65, Cambridge University Press, Cambridge, 2006.
10 K. Baur and T. Brustle, The quivers of the hereditary algebras of type A, arXiv:1312.2995v1 [math.RT] 10 Dec 2013.