General presentations of algebras

For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two theorems about a general presentation, one on its subrepresentations and the other on its canonical decomposition. As a special case, we consider rig...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2015-06, Vol.278, p.210-237
Main Authors: Derksen, Harm, Fei, Jiarui
Format: Article
Language:English
Subjects:
Canonical decomposition
Cluster complex
General presentation
Quiver with potential
Representation of algebra
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Summary:For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two theorems about a general presentation, one on its subrepresentations and the other on its canonical decomposition. As a special case, we consider rigid presentations. We show how to complete a rigid presentation and study the number of nonisomorphic direct summands and different complements. Based on that, we construct a simplicial complex governing the canonical decompositions of rigid presentations and provide some examples.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2015.03.012