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Separating Splitting Tilting Modules and Hereditary Algebras

Published online by Cambridge University Press:  20 November 2018

Ibrahim Assem
Ibrahim Assem*
Affiliation:
Fakultät Für Mathematik Universität Bielefeld 4800, Bielefeld 1 Federal Republic of Germany
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Abstract

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Let A be a finite-dimensional algebra over an algebraically closed field. By module is meant a finitely generated right module. A module T ^ is called a tilting module if and there exists an exact sequence 0 → A^ → T' → T" → 0 with T'. T" direct sums of summands of T. Let B = End T^·T^ is called separating (respectively, splitting) if every indecomposable A-module M (respectively, B-module N) is such that either Hom^(T,M) = 0 or (respectively, N ⊗ T = 0 or . We prove that A is hereditary provided the quiver of A has no oriented cycles and every separating tilting module is splitting.

Keywords

Primary 16A46secondary 16A64Representations of hereditary algebrastilting modules

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 177 - 181
Copyright
Copyright © Canadian Mathematical Society 1987

References

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