General Presentations of Algebras

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.

24 pages, 3 figures. V2. Section 2 is new. Some argument was simplified. New examples, references were added, and typos were corrected. V3. Final version to appear. Adv. Math. 2015

References in corpus (2)

• General Presentations of Algebras
• Generic decompositions and semi-invariants for string algebras

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