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arXiv · 0911.4913

General Presentations of Algebras

Harm Derksen·Jiarui Fei
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Abstract

For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions 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.

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Harm Derksen, Jiarui Fei. 2009-11-25. General Presentations of Algebras. https://arxiv.org/abs/0911.4913

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