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.
Keywords
Cite
@article{arxiv.0911.4913,
title = {General Presentations of Algebras},
author = {Harm Derksen and Jiarui Fei},
journal= {arXiv preprint arXiv:0911.4913},
year = {2015}
}
Comments
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