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Abelian Groups and Modules pp 517–531Cite as

The Representation Type of Group Algebras

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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 287))

Abstract

Throughout this paper we use the term algebra to mean finite-dimensional algebra over a fixed algebraically closed field K and the term module to mean finitely generated right module. Algebras, as is usual in representation theory, are assumed to be basic. For any algebra A we will denote by mod A the category of finitely generated A-modules and by ind A the full subcategory of mod A consisting of all indecomposable modules.

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References

  1. Drozd, O.A., On tame and wild matrix problems, in Matrix problems, Kiev, 1977, 104–114.

    Google Scholar 

  2. Drozd, O.A., Tame and wild matrix problems, in Representations and quadratic forms, Kiev, 1979, 39–74.

    Google Scholar 

  3. Higman, D., Indecomposable representations at characteristic p, Duke Math. 3. 21,377–381, 1954.

    Article  MathSciNet  Google Scholar 

  4. Meltzer, H., Skowronski, A., Group algebras of finite representation type, Math. Z. 182, 129–148, 1983

    Article  MATH  MathSciNet  Google Scholar 

  5. Meltzer, H., Skowroriski, A., Correction to “Group algebras of finite representation type”, Math. Z., to appear.

    Google Scholar 

  6. Krugliak, S.A., Representations of the (P#P) group over a field of charakteristic p, Dokl. Akad. Nauk SSSR 153, 1253–1256, 1963.

    MathSciNet  Google Scholar 

  7. Brenner, S., Modular representations of p groups, J. Algebra 15, 89–102, 1970.

    Article  MATH  MathSciNet  Google Scholar 

  8. Bondarenko, V.M., Representations of dihedral groups over a field of characteristic 2. Math. Sbornik 96, 63–74, 1975.

    MathSciNet  Google Scholar 

  9. Ringel, C.M., The indecomposable representations of dihedral 2-groups, Math. Ann. 214, 19–34, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  10. Bondarenko, V.M., Drozd, O.A., Representation type of finite groups, Zap. Naučn. Sem. LOMI 71, 24–41, 1977.

    MATH  MathSciNet  Google Scholar 

  11. Ringel, C.M., Tame group algebras, in Darstellungstheorie, Endlich Dimensionaler Algebren, Oberwolfach, 1977, 92–95.

    Google Scholar 

  12. Gabriel, P., Auslander-Reiten sequences and representation-finite algebras, Lecture Notes in Math. 831, 1980, 1–71.

    Article  MathSciNet  Google Scholar 

  13. Bongartz, K., Gabriel, P., Covering spaces in representation theory, Invent. math. 65, 331–378, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  14. Gabriel, P., The universal cover of a representation-finite algebra. Lecture Notes in Math. 903, 1981, 68–105.

    Article  MathSciNet  Google Scholar 

  15. Riedtmann, Chr., Algebren, Darstellungsköcher, Überlagerungen and zurück, Comment. Math. Helv. 55, 199–224, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  16. Dowbor, P., Skowronski, A., On Galois coverings of tame algebras, to appear.

    Google Scholar 

  17. Dowbor, P., Skowronski, A., Galois coverings of algebras of infinite representation type, to appear.

    Google Scholar 

  18. Ringel, C.M., Tame algebras, Lecture Notes in Math. 831 1980, 137–287.

    Article  MathSciNet  Google Scholar 

  19. Dowbor, P, Skowronski, A., Some remarks on the representation type of locally bounded categories, to appear

    Google Scholar 

  20. Gabriel, P., Indecomposable representations II, Symposia Math. 11, 81–104, 1973.

    MathSciNet  Google Scholar 

  21. Dlab, V., Ringel, C.M., Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 173, 1976

    Google Scholar 

  22. Waschbüsch, J., Universal coverings of selfinjective algebras, Lecture Notes in Math. 903, 1981, 331–349.

    Article  Google Scholar 

  23. Auslander, M., Reiten, I., Representation theory of artin algebras III, Almost split sequences, Comm. Algebra 3, 239–294, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  24. Auslander, M., Reiten, I., Representation theory of artin algebras IV, Invariants given by almost split sequences, Comm. Algebra 5, 443–518.

    Google Scholar 

  25. Nazarova, L.A., Rojter, A.V., Kategorielle Matrizen-Probleme und die Brauer-Thrall-Vermuttung, Mitt. Math. Sem. Giessen 115, 1975, 1–153.

    Google Scholar 

  26. Simson, D., Vector space categories, right peak rings and their socle projective modules, 3. Algebra, to appe ar.

    Google Scholar 

  27. Simson, D., Representations of partially ordered sets, vector space categories and socle projective modales, Paderborn, 1983.

    Google Scholar 

  28. Simson, D., A module-theoretical approach to vector space categories, to appear.

    Google Scholar 

  29. Nazarova, L.A., Rojter, A.V., Representations of partially ordered sets, Zap. Naučn. Sem. LOMI 28, 1972, 5–31.

    Google Scholar 

  30. Pogorzały, Z., Skowronski, A., On algebras whose indecomposable modules are multiplicity-free, Proc. London Math. Soc. 47, 463–479, 1983.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Nicholas Copernicus University, 87-100, Toruń, Poland

    Andrzej Skowroński

Authors
  1. Andrzej Skowroński
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Editor information

Editors and Affiliations

  1. Universität Essen, Germany

    R. Göbel

  2. Universita’ di Padova, Italy

    C. Metelli  & A. Orsatti  & 

  3. Universita’ di Udine, Italy

    L. Salce

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© 1984 Springer-Verlag Wien

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Skowroński, A. (1984). The Representation Type of Group Algebras. In: Göbel, R., Metelli, C., Orsatti, A., Salce, L. (eds) Abelian Groups and Modules. International Centre for Mechanical Sciences, vol 287. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2814-5_37

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  • DOI: https://doi.org/10.1007/978-3-7091-2814-5_37

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81847-3

  • Online ISBN: 978-3-7091-2814-5

  • eBook Packages: Springer Book Archive

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