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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The geometry of uniserial representations
of finite dimensional algebras.
III: Finite uniserial type


Author: Birge Huisgen-Zimmermann
Journal: Trans. Amer. Math. Soc. 348 (1996), 4775-4812
MSC (1991): Primary 16G10, 16G20, 16G60, 16P10
MathSciNet review: 1344208
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Abstract: A description is given of those sequences $\mathbf {S}= (S(0),S(1),\dots ,S(l))$ of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors $S(0),\dots ,\linebreak S(l)$. Necessary and sufficient conditions for an algebra to permit only a finite number of isomorphism types of uniserial modules are derived. The main tools in this investigation are the affine algebraic varieties parametrizing the uniserial modules with composition series $ \mathbf {S}$.


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Additional Information

Birge Huisgen-Zimmermann
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: birge@math.ucsb.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01575-9
PII: S 0002-9947(96)01575-9
Received by editor(s): November 14, 1994
Additional Notes: This research was partially supported by a National Science Foundation grant.
Article copyright: © Copyright 1996 American Mathematical Society