Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On homomorphisms from a fixed representation to a general representation of a quiver

Author: William Crawley-Boevey
Journal: Trans. Amer. Math. Soc. 348 (1996), 1909-1919
MSC (1991): Primary 16G20; Secondary 14M15
MathSciNet review: 1348149
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the dimension of the space of homomorphisms from a given representation $X$ of a quiver to a general representation of dimension vector $\beta$. We prove a theorem about this number, and derive two corollaries concerning its asymptotic behaviour as $\beta$ increases. These results are related to work of A. Schofield on homological epimorphisms from the path algebra to a simple artinian ring.

References [Enhancements On Off] (What's this?)

  • N. Bourbaki, Algèbre Commutative, Hermann, Paris, 1961–83.
  • Michel Demazure and Pierre Gabriel, Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970 (French). Avec un appendice Corps de classes local par Michiel Hazewinkel. MR 0302656
  • D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Math. 150, Springer-Verlag, New York, 1995.
  • Claudio Procesi, Rings with polynomial identities, Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, 17. MR 0366968
  • A. H. Schofield, Representation of rings over skew fields, London Mathematical Society Lecture Note Series, vol. 92, Cambridge University Press, Cambridge, 1985. MR 800853
  • Aidan Schofield, General representations of quivers, Proc. London Math. Soc. (3) 65 (1992), no. 1, 46–64. MR 1162487, DOI

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 16G20, 14M15

Retrieve articles in all journals with MSC (1991): 16G20, 14M15

Additional Information

William Crawley-Boevey
Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England
MR Author ID: 230720

Received by editor(s): July 21, 1995
Article copyright: © Copyright 1996 American Mathematical Society