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Decomposition Classes for Representations of Tame Quivers

✍ Scribed by Klaus Bongartz; Dirk Dudek

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 163 KB
Volume: 240
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8705

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✦ Synopsis

For the variety of representations of a tame quiver, we describe a finite stratification into smooth subvarieties that are invariant under the group of base changes and that admit smooth rational geometric quotients. A stratum consists of all representations that differ only in the parameters of the homogeneous indecomposable direct summands. For the special case of the loop our definition coincides Ž Ž.

. with the well-known bundles V. I. Arnold, Uspekhi Mat. Nauk 26 1971 , 101᎐114 Ž or decomposition classes of matrices W. Borho and H. Kraft, Comment. Math. Ž . . Hel¨. 54 1979 , 61᎐104 . ᮊ 2001 Academic Press w x partition q . Interpreting a matrix as a k X module, we see that two

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