Skip to main content

Introduction to the Representation Theory of Finite-Dimensional Algebras: The Functorial Approach

  • Chapter
  • First Online:
Homological Methods, Representation Theory, and Cluster Algebras

Part of the book series: CRM Short Courses ((CRMSC))

  • 1179 Accesses

Abstract

These are the notes of a course given at the CIMPA School “Homological Methods, Representation Theory and Cluster Algebras,” Mar del Plata, Argentina, 2016. The aim of this brief course is to give an introduction to the functorial approach to the representation theory of finite-dimensional algebras, developed by Maurice Auslander and Idun Reiten, and is strongly based on the work “A functorial approach to representation theory,” by M. Auslander (Representations of Algebras. Springer, Berlin, 1981) [4].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anderson, F.W., Fuller, K.R.: Rings and Categories of Modules, Grad. Texts in Math., vol. 13, 2nd edn. Springer, New York (1992). DOI https://doi.org/10.1007/978-1-4612-4418-9

  2. Auslander, M.: Representation theory of Artin algebras. I. Comm. Algebra 1(3), 177–268 (1974). DOI https://doi.org/10.1080/00927877408548230

  3. Auslander, M.: Representation theory of Artin algebras. II. Comm. Algebra 1(4), 269–310 (1974). DOI https://doi.org/10.1080/00927877409412807

  4. Auslander, M.: A functorial approach to representation theory. In: M. Auslander, E. Lluis (eds.) Representations of Algebras (Puebla, 1980), Lecture Notes in Math., vol. 903, pp. 105–179. Springer, Berlin (1981)

    Google Scholar 

  5. Auslander, M., Reiten, I.: Representation theory of Artin algebras. III. Almost split sequences. Comm. Algebra 3(3), 239–294 (1975). DOI https://doi.org/10.1080/00927877508822046

  6. Auslander, M., Reiten, I.: Representation theory of Artin algebras. IV. Invariants given by almost split sequences. Comm. Algebra 5(5), 443–518 (1977). DOI https://doi.org/10.1080/00927877708822180

  7. Auslander, M., Reiten, I.: Representation theory of Artin algebras. V. Methods for computing almost split sequences and irreducible morphisms. Comm. Algebra 5(5), 519–554 (1977). DOI https://doi.org/10.1080/00927877708822181

  8. Auslander, M., Reiten, I.: Representation theory of Artin algebras. VI. A functorial approach to almost split sequences. Comm. Algebra 6(3), 257–300 (1978). DOI https://doi.org/10.1080/00927877808822246

  9. Auslander, M., Reiten, I., Smalø, S.O.: Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math., vol. 36. Cambridge Univ. Press, Cambridge (1995). DOI https://doi.org/10.1017/CBO9780511623608

  10. Cartan, H., Eilenberg, S.: Homological Algebra. Princeton Landmarks Math. Princeton Univ. Press, Princeton, NJ (1999). Reprint of the 1956 original

    Google Scholar 

  11. Hilton, P.J., Stammbach, U.: A Course in Homological Algebra, Graduate Texts in Mathematics, vol. 4, 2nd edn. Springer, New York (1997). DOI https://doi.org/10.1007/978-1-4419-8566-8

  12. Reiten, I., Smalø, S.O., Solberg, Ø. (eds.): Selected works of Maurice Auslander, Collect. Works, vol. 10. Amer. Math. Soc., Providence, RI (1999)

    Google Scholar 

Download references

Acknowledgements

The author thanks the organizers of the CIMPA School “Homological Methods, Representation Theory and Cluster Algebras” and the friends and students of the Mathematics Department of the Universidad Nacional de Mar del Plata for their warm hospitality. She also acknowledges partial support from CONICET and from Universidad Nacional del Sur, Argentina

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to María Inés Platzeck .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Platzeck, M.I. (2018). Introduction to the Representation Theory of Finite-Dimensional Algebras: The Functorial Approach. In: Assem, I., Trepode, S. (eds) Homological Methods, Representation Theory, and Cluster Algebras. CRM Short Courses. Springer, Cham. https://doi.org/10.1007/978-3-319-74585-5_1

Download citation

Publish with us

Policies and ethics