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Strongly simply connected Auslander algebras

Published online by Cambridge University Press:  18 May 2009

Ibrahim Assem  and
Peter Brown
Ibrahim Assem
Affiliation:
Département de Mathématiques et d'Informatique, Université de Sherbrooke, Sherbrooke (Québec) J1K 2R1, Canada
Peter Brown
Affiliation:
Département de Mathématiques et d'Informatique, Université de Sherbrooke, Sherbrooke (Québec) J1K 2R1, Canada
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Let k be an algebraically closed field. By an algebra is meant an associative finite dimensional k-algebra A with an identity. We are interested in studying the representation theory of Λ, that is, in describing the category mod Λ of finitely generated right Λ-modules. Thus we may, without loss of generality, assume that Λ is basic and connected. For our purpose, one strategy consists in using covering techniques to reduce the problem to the case where the algebra is simply connected, then in solving the problem in this latter case. This strategy was proved efficient for representation-finite algebras (that is, algebras having only finitely many isomorphism classes of indecomposable modules) and representation-finite simply connected algebras are by now well-understood: see, for instance [5], [7],[8]. While little is known about covering techniques in the representation-infinite case, it is clearly an interesting problem to describe the representation-infinite simply connected algebras. The objective of this paper is to give a criterion for the simple connectedness of a class of (mostly representationinfinite) algebras.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 1 , January 1997 , pp. 21 - 27
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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