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)

 
 

 

Optimal filtrations on representations of finite dimensional algebras


Author: Lieven Le Bruyn
Journal: Trans. Amer. Math. Soc. 353 (2001), 411-426
MSC (2000): Primary 16G20, 16R30
DOI: https://doi.org/10.1090/S0002-9947-00-02590-3
Published electronically: September 13, 2000
MathSciNet review: 1707199
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We present a representation theoretic description of the non-empty strata in the Hesselink stratification of the nullcone of representations of quivers. We use this stratification to define optimal filtrations on representations of finite dimensional algebras. As an application we investigate the isomorphism problem for uniserial representations.


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

  • 1. K. Bongartz and B. Huisgen-Zimmermann, Varieties of uniserial representations IV : Kinship to geometric quotients, preprint UCSB (1997)
  • 2. W. Hesselink, Desingularization of varieties of nullforms, Invent. Math. 55 (1977), 141-163 MR 81b:14025
  • 3. B. Huisgen-Zimmermann, The geometry of uniserial representations of finite dimensional algebras I, J. Pure Appl. Algebra 127 (1998), 39-72 MR 99b:16020
  • 4. B. Huisgen-Zimmermann, The geometry of uniserial representations of finite dimensional algebras III : Finite uniserial type, Trans. Amer. Math. Soc. 348 (1996) 4775-4812 MR 97f:16027
  • 5. G. Kempf, Instability in invariant theory, Ann. of Math. 108 (1978), 299-316 MR 80c:20057
  • 6. A. King, Moduli of representations of finite dimensional algebras, Quart. J. Math. Oxford 45 (1994) 515-530 MR 96a:16009
  • 7. F.C. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Princeton Math. Notes 31 (1984) MR 86i:58050
  • 8. H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspects of Mathematics D1, Vieweg (1984) MR 86j:14006
  • 9. H. Kraft, Geometric methods in invariant theory, Representations of Algebras, Eds. M. Auslander and E. Lluis, Springer LNM 944 (1982) 180-258 MR 84c:14007
  • 10. L. Le Bruyn, Nilpotent representations, J. Alg. 197 (1997), 153-177 MR 98k:14070
  • 11. A. Schofield, General representations of quivers, Proc. LMS 65 (1992) 46-64 MR 93d:16014
  • 12. P. Slodowy, Die Theorie der optimalen Einparametergruppen für instabile Vektoren, DMV Seminar 13 (1989) Birkhäuser-Verlag, pp. 115-131 MR 91m:14074

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 16G20, 16R30

Retrieve articles in all journals with MSC (2000): 16G20, 16R30


Additional Information

Lieven Le Bruyn
Affiliation: Departement Wiskunde UIA Universiteitsplein 1, B-2610 Antwerp, Belgium
Email: lebruyn@uia.ua.ac.be

DOI: https://doi.org/10.1090/S0002-9947-00-02590-3
Received by editor(s): May 26, 1998
Received by editor(s) in revised form: April 30, 1999
Published electronically: September 13, 2000
Additional Notes: The author is a research director at the FWO (Belgium)
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society