Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-18T13:15:47.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Injective Representations of Infinite Quivers. Applications

Published online by Cambridge University Press:  20 November 2018

E. Enochs ,
S. Estrada  and
J. R. García Rozas
E. Enochs
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027, U.S.A., [email protected]
S. Estrada
Affiliation:
Departamento de Matemática Aplicada, Universidad de Murcia, Campus del Espinardo, Espinardo (Murcia) 30100, Spain, [email protected]
J. R. García Rozas
Affiliation:
Departamento de Álgebra y A. Matemático, Universidad de Almería, Almería 04071, Spain, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and describe Gorenstein injective and projective representations of barren trees.

Keywords

16G2018A40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 2 , 01 April 2009 , pp. 315 - 335
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Assem, I., Simson, D. and Skowroński, A., Elements of the representation theory of associative algebras. Vol. 1. Techniques of representation theory. London Mathematical Society Student Texts 65, Cambridge University Press, Cambridge, 2006.Google Scholar
[2] Enochs, E. and Estrada, S.. Projective representations of quivers. Comm. Algebra. 33(2005), no. 10, 3467–3478.Google Scholar
[3] Enochs, E. and Estrada, S., Relative homological algebra in the category of quasi-coherent sheaves. Adv. Math. 194(2005), no. 2, 284–295.Google Scholar
[4] Enochs, E., Estrada, S., and Garćıa Rozas, J. R., Gorenstein categories and Tate cohomology on projective schemes. Math. Nachr. 281(2008), no. 4, 525–540.Google Scholar
[5] Enochs, E., Estrada, S., Garćıa Rozas, J. R., and Iacob, A.. Gorenstein quivers. Arch. Math (Basel) 88(2007), no. 3, 199–206.Google Scholar
[6] Enochs, E., Garćıa Rozas, J. R., Oyonarte, L., and Park, S., Noetherian quivers. Quaest. Math. 25(2002), no. 4, 531–538.Google Scholar
[7] Enochs, E. and Herzog, I., A homotopy of quiver morphisms with applications to representations. Canad. J. Math. 51(1999), no. 2, 294–308.Google Scholar
[8] Enochs, E. and Jenda, O., Relative homological algebra. de Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin, 2000.Google Scholar
[9] Enochs, E., Oyonarte, L., and Torrecillas, B., Flat covers and flat representations of quivers. Comm. Algebra. 32(2004), no. 4, 1319–1338.Google Scholar
[10] Estrada, S.,Monomial algebras over infinite quivers. Applications to N-complexes of modules. Comm. Algebra 35(2007), no. 10, 3214–3225.Google Scholar
[11] Gabriel, P., Unzerlegbare Darstellungen I. Manuscripta Math. 6(1972), 71–103.Google Scholar
[12] Hovey, M.,Model categories. Mathematical Surveys and Monographs 63, American Mathematical Society, Providence, RI, 1999.Google Scholar
[13] Iwanaga, Y., On rings with finite self-injective dimension. Comm. Algebra 7(1979), no. 4, 393–414.Google Scholar
[14] Le Bruyn, L. and Procesi, C., Semisimple representations of quivers. Trans. Amer. Math. Soc. 317(1990), no. 2, 585–598.Google Scholar
[15] Mac Lane, S., Categories for the working mathematician. Second ed., Graduate Texts in Mathematics 5, Springer-Verlag, New York, 1998.Google Scholar