Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T10:16:05.642Z Has data issue: false hasContentIssue false
  • English
  • Français

Kac's Theorem for equipped graphs and for maximal rank representations

Part of: Representation theory of rings and algebras

Published online by Cambridge University Press:  17 April 2013

William Crawley-Boevey
William Crawley-Boevey*
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK ([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.

We give two generalizations of Kac's Theorem on representations of quivers. One is to representations of equipped graphs by relations, in the sense of Gelfand and Ponomarev. The other is to representations of quivers in which certain of the linear maps are required to have maximal rank.

Keywords

representations of quiversrepresentations of graphsKac's Theorem

MSC classification

Secondary: 16G20: Representations of quivers and partially ordered sets
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 2 , June 2013 , pp. 443 - 447
Copyright
Copyright © Edinburgh Mathematical Society 2013

References

1.Gabriel, P., Unzerlegbare Darstellungen, I, Manuscr. Math. 6 (1972), 71–103.CrossRefGoogle Scholar
2.Gelfand, I. M. and Ponomarev, V. A., Gabriel's theorem is also valid for representations of equipped graphs by relations, Funct. Analysis Applic. 15 (1981), 132–133.CrossRefGoogle Scholar
3.Kac, V. G., Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), 57–92.CrossRefGoogle Scholar
4.Kac, V. G., Root systems, representations of quivers and invariant theory, in Invariant Theory, Montecatini, 1982 (ed. Gherardelli, F.), Lecture Notes in Mathematics, Volume 996, pp. 74–108 (Springer, 1983).Google Scholar
5.Wiedemann, M., Quiver representations of maximal rank type and an application to representations of a quiver with three vertices, Bull. Lond. Math. Soc. 40 (2008), 479–492.CrossRefGoogle Scholar