Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Interpolation and Comparison Methods in the Mean Field Spin Glass Model Read chapter Read first chapter

2014 | OriginalPaper | Chapter

14. Dynkin and Extended Dynkin Diagrams

Author : Idun Reiten

Published in: Trends in Contemporary Mathematics

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper we give a survey of some of the occurrences of Dynkin and extended Dynkin diagrams in algebra. It is based on my lecture at the INdAM day in 2009, with some later developments included.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Birational Geometry of Projective Varieties and Directed Graphs
next chapter Tracking Control of 1D Scalar Conservation Laws in the Presence of Shocks
Literature
1.
I. Assem, D. Simson, A. Skowroński, Elements of the Representation Theory of Associative Algebras. Vol. 1. Techniques of Representation Theory. London Mathematical Society Student Texts, vol. 65 (Cambridge University Press, Cambridge, 2006). pp. x+458
2.
3.
M. Auslander, Isolated singularities and existence of almost split sequences, in Representation Theory, II, Ottawa, 1984. Lecture Notes in Mathematics, vol. 1178 (Springer, Heidelberg, 1986), pp. 194–242
4.
M. Auslander, I. Reiten, Representation theory of Artin algebras. III. Almost split sequences. Commun. Algebra 3, 239–294 (1975)MATHMathSciNet
5.
6.
M. Auslander, I. Reiten, S.O. Smalø, Representation Theory of Artin Algebras. Cambridge Studies in Advanced Mathematics, vol. 36 (Cambridge University Press, Cambridge, 1995), pp. xiv+423
7.
D. Baer, Homological properties of wild hereditary Artin algebras, in Representation Theory, I, Ottawa, 1984. Lecture Notes in Mathematics, vol. 1177 (Springer, New York, 1986), pp. 1–12
8.
9.
I.N. Bernstein, I.M. Gelfand, V.A. Ponomarev, Coxeter functors, and Gabriel’s theorem (Russian). Uspehi Mat. Nauk 28, 19–33 (1973)MATHMathSciNet
10.
A. Björner, F. Brenti, Combinatorics of Coxeter Groups. Graduate Texts in Mathematics, vol. 231 (Springer, New York, 2005), pp. xiv+363
11.
A.B. Buan, I. Reiten, Acyclic quivers of finite mutation type. Int. Math. Res. Not. 12804, 10 (2006)MathSciNet
12.
A.B. Buan, R.J. Marsh, M. Reineke, I. Reiten, G. Todorov, Tilting theory and cluster combinatorics. Adv. Math. 204, 572–618 (2006)CrossRefMATHMathSciNet
13.
14.
A.B. Buan, R.J. Marsh, I. Reiten, G. Todorov, Clusters and seeds in acyclic cluster algebras, with an appendix coauthored in addition by P. Caldero and B. Keller. Proc. Am. Math. Soc. 135, 3049–3060 (2007)CrossRefMATHMathSciNet
15.
16.
A.B. Buan, O. Iyama, I. Reiten, J. Scott, Cluster structures for 2-Calabi-Yau categories and unipotent groups. Compos. Math. 145, 1035–1079 (2009)CrossRefMATHMathSciNet
17.
P. Caldero, B. Keller, From triangulated categories to cluster algebras. II. Ann. Sci. École Norm. Sup. (4) 39, 983–1009 (2006)
18.
19.
V. Dlab, C.M. Ringel, The preprojective algebra of a modulated graph, in Representation Theory, II. Proceedings of Second International Conference, Carleton University, Ottawa, 1979. Lecture Notes in Mathematics, vol. 832 (Springer, Berlin/Heidelberg, 1980), pp. 216–231
20.
A. Felikson, M. Shapiro, P. Tumarkin, Skew-symmetric cluster algebras of finite mutation type. J. Eur. Math. Soc. (JEMS) 14, 1135–1180 (2012)CrossRefMATHMathSciNet
21.
22.
S. Fomin, A. Zelevinsky, Cluster algebras. II. Finite type classification. Invent. Math. 154, 63–121 (2003)MATHMathSciNet
23.
24.
25.
I.M. Gelfand, V.A. Ponomarev, Model algebras and representations of graphs. Funct. Anal. Appl. 13, 157–166 (1980)
26.
D. Happel, U. Preiser, C.M. Ringel, Vinberg’s characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules, in Representation Theory, II. Proceedings of Second International Conference, Carleton University, Ottawa, 1979. Lecture Notes in Mathematics, vol. 832 (Springer, Berlin/Heidelberg, 1980), pp. 280–294
27.
28.
29.
H. Lenzing, Homological transfer from finitely presented to infinite modules, in Abelian Group Theory. Lecture Notes in Mathematics, vol. 1006 (Springer, Berlin/Heidelberg, 1983), pp. 734–761
30.
J. McKay, Graphs, singularities, and finite groups, in The Santa Cruz Conference on Finite Groups, University of California, Santa Cruz, 1979. Proceedings of Symposia in Pure Mathematics, vol. 37 (American Mathematical Society, Providence, 1980), pp. 183–186
31.
S. Oppermann, I. Reiten, H. Thomas, Quotient closed subcategories of quiver representations (2012). arXiv:1205.3268, Compos. Math. (to appear)
32.
I. Reiten, Dynkin diagrams and the representation theory of algebras. Not. Am. Math. Soc. 44, 546–556 (1997)MATHMathSciNet
33.
C.M. Ringel, Tame Algebras and Integral Quadratic Forms. Lecture Notes in Mathematics, vol. 1099 (Springer, Berlin, 1984), pp. xiii+376
34.
35.
G. Todorov, Almost split sequences for TrD-periodic modules, in Representation Theory, II. proceedings of the Second International Conference, Carleton University, Ottawa, 1979. Lecture Notes in Mathematics, vol. 832 (Springer, Berlin/Heidelberg, 1980), pp. 600–631
Metadata
Title
Dynkin and Extended Dynkin Diagrams
Author
Idun Reiten
Copyright Year
2014
Book
Trends in Contemporary Mathematics

Print ISBN: 978-3-319-05253-3

Electronic ISBN: 978-3-319-05254-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-05254-0_14

Premium Partner

    Image Credits