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Tilting modules and a theorem of Hoshino

Published online by Cambridge University Press:  18 May 2009

Ibrahim Assem  and
Otto Kerner
Ibrahim Assem
Affiliation:
Ibrahim Assem Mathématiques Et InformatiqueUniversité De SherbrookeSherbrooke, Quebec Canada, J1K 2R1
Otto Kerner
Affiliation:
Otto Kerner Mathematisches InstitutHeinrich Heine UniversitätUniversitätstr. 1 D-4000 Düsseldorf 1 Federal Republic of Germany
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Let k be an algebraically closed field, and A a finite dimensional k-algebra, which we shall assume, without loss of generality, to be basic and connected. By module is meant throughout a finitely generated right A-module. Following Happel and Ringel [10], we shall say that a module Tλ is a tilting (respectively, cotilting) module if it satisfies the following three conditions:

(1)

(2)

(3) the number of non-isomorphic indecomposable summands of T equals the rank of the Grothendieck group K0(A) of A.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 1 , January 1993 , pp. 69 - 77
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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