## Optimal filtrations on representations of finite dimensional algebras

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**353**(2001), 411-426 Request permission

## 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

- K. Bongartz and B. Huisgen-Zimmermann,
*Varieties of uniserial representations IV : Kinship to geometric quotients*, preprint UCSB (1997) - Wim H. Hesselink,
*Desingularizations of varieties of nullforms*, Invent. Math.**55**(1979), no. 2, 141–163. MR**553706**, DOI 10.1007/BF01390087 - Birge Huisgen-Zimmermann,
*The geometry of uniserial representations of finite-dimensional algebra. I*, J. Pure Appl. Algebra**127**(1998), no. 1, 39–72. MR**1609508**, DOI 10.1016/S0022-4049(96)00184-3 - Birge Huisgen-Zimmermann,
*The geometry of uniserial representations of finite-dimensional algebras. III. Finite uniserial type*, Trans. Amer. Math. Soc.**348**(1996), no. 12, 4775–4812. MR**1344208**, DOI 10.1090/S0002-9947-96-01575-9 - George R. Kempf,
*Instability in invariant theory*, Ann. of Math. (2)**108**(1978), no. 2, 299–316. MR**506989**, DOI 10.2307/1971168 - A. D. King,
*Moduli of representations of finite-dimensional algebras*, Quart. J. Math. Oxford Ser. (2)**45**(1994), no. 180, 515–530. MR**1315461**, DOI 10.1093/qmath/45.4.515 - Frances Clare Kirwan,
*Cohomology of quotients in symplectic and algebraic geometry*, Mathematical Notes, vol. 31, Princeton University Press, Princeton, NJ, 1984. MR**766741**, DOI 10.2307/j.ctv10vm2m8 - Hanspeter Kraft,
*Geometrische Methoden in der Invariantentheorie*, Aspects of Mathematics, D1, Friedr. Vieweg & Sohn, Braunschweig, 1984 (German). MR**768181**, DOI 10.1007/978-3-322-83813-1 - Hanspeter Kraft,
*Geometric methods in representation theory*, Representations of algebras (Puebla, 1980) Lecture Notes in Math., vol. 944, Springer, Berlin-New York, 1982, pp. 180–258. MR**672117** - Lieven Le Bruyn,
*Nilpotent representations*, J. Algebra**197**(1997), no. 1, 153–177. MR**1480781**, DOI 10.1006/jabr.1997.7122 - Aidan Schofield,
*General representations of quivers*, Proc. London Math. Soc. (3)**65**(1992), no. 1, 46–64. MR**1162487**, DOI 10.1112/plms/s3-65.1.46 - Hanspeter Kraft, Peter Slodowy, and Tonny A. Springer (eds.),
*Algebraische Transformationsgruppen und Invariantentheorie*, DMV Seminar, vol. 13, Birkhäuser Verlag, Basel, 1989 (German). MR**1044582**, DOI 10.1007/978-3-0348-7662-9

## Additional Information

**Lieven Le Bruyn**- Affiliation: Departement Wiskunde UIA Universiteitsplein 1, B-2610 Antwerp, Belgium
- Email: lebruyn@uia.ua.ac.be
- 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)
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1707199