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Bulletin of the London Mathematical Society Advance Access originally published online on November 4, 2008
Bulletin of the London Mathematical Society 2009 41(1):16-26; doi:10.1112/blms/bdn091
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© 2008 London Mathematical Society

The Gabriel–Roiter measure for radical-square zero algebras

Bo Chen

Hausdorff Center for Mathematics
Universität Bonn
Endenicher Allee 60
(LWK Neubau)
53115 Bonn
Germany

Received 18 December 2007. Revision received 10 July 2008.

Let {Lambda} be a radical-square zero algebra over an algebraically closed field k with radical r, and let Formula be the associated hereditary algebra. There is an explicit functor F: mod {Lambda} -> mod {Gamma}, which induces a stable equivalence. In this paper, it will be proved that the functor F preserves the Gabriel–Roiter (GR) measures and the GR factors. Thus the GR measure for {Lambda} can be studied by the use of F and known facts for hereditary algebras. In particular, the middle terms of the Auslander–Reiten sequences ending at the GR factors and the relationship between the preprojective partition for {Lambda} and the take-off {Lambda}-modules will be investigated.

2000 Mathematics Subject Classification 16G20, 16G70.


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