Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2019; 34(3): 701-718

Online first article July 8, 2019      Printed July 31, 2019

https://doi.org/10.4134/CKMS.c180226

Copyright © The Korean Mathematical Society.

The $U$-projective resolution of modules over path algebras of types $A_n$ and $\tilde{A}_n$

Karin Baur, Yudi Mahatma, Intan Muchtadi-Alamsyah

Institut f\"{u}r Mathematik und Wissenschaftliches Rechnen Universit\"{a}t Graz, Jalan Ganesha 10; Jalan Ganesha 10

Abstract

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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

MSC numbers: 16G06, 13D06, 13C10

Supported by: The second author was funded by Sandwich-like Pro-gram from Directorate General of Resources for Sciences, Technology, and
Higher Education; Ministry of Research and Technology Republic of Indone-sia, carried out from October 2017 to January 2018 at the University of Leeds, United Kingdom. The first and third authors were funded by ASEA UNINET Program 2016. This research was also partially funded by Hibah Desentralisasi DIKTI 2017-2018.

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