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STABLE EQUIVALENCE AND GENERIC MODULES

Published online by Cambridge University Press:  23 October 2000

HENNING KRAUSE  and
GRZEGORZ ZWARA
HENNING KRAUSE
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany; e-mail: henning@mathematik.uni-bielefeld.de
GRZEGORZ ZWARA
Affiliation:
Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland; e-mail: gzwara@mat.uni.torun.pl
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Abstract

Let Λ and Γ be finite dimensional algebras. It is shown that any stable equivalence f [ratio ] mod Λ → mod Γ between the categories of finitely generated modules induces a bijection M [map ] Mf between the sets of isomorphism classes of generic modules over Λ and Γ such that the endolength of Mf is bounded by the endolength of M up to a scalar which depends only on f. Using Crawley-Boevey's characterization of tame representation type in terms of generic modules, one obtains as a consequence a new proof for the fact that a stable equivalence preserves tameness. This proof also shows that polynomial growth is preserved.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 5 , September 2000 , pp. 615 - 618
Copyright
© The London Mathematical Society 2000

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Footnotes

The results in this paper evolved during a visit of the first author to Toruń. The second author gratefully acknowledges support from Polish Scientific Grant KBN No. 2 PO3A 012 14.