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

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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.

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.

참고문헌 (10)

  1. Assem, D. Simson, "Elements of the representation theory of associative algebras. Vol. 1" (2006), Cambridge University Press
  2. , 2013
  3. , 2015
  4. B. Davvaz, "A note on exact sequences", Bull. Malaysian Math. Soc. (2), 22(1), pp.53~56 (1999)
  5. B. Davvaz, "A generalization of homological algebra", 대한수학회지, 39(6), pp.881~898 (2002), 대한수학회
  6. Faisal Faisal, "Auslander Reiten Quiver of Nakayama Algebra type Dynkin Graph An", Journal of Mathematical and Fundamental Sciences, 45(1), pp.1~16 (2013), The Institute for Research and Community Services (LPPM) ITB[DOI]
  7. Y. Mahatma, "Construction of U-extension module", AIP Conference Proceedings 1867 (2017)
  8. J. J. Rotman, "An Introduction to Homological Algebra" (2009), Springer
  9. Ouvrages de Math-ematiques de la SMC, "Quiver Representations, CMS Books in Mathematics", pp.2014, R. Schier
  10. M. Warkentin, "Fadenmoduln uber A und cluster-kombinatorik", pp.2008

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