General Presentations of Algebras.

[摘要] For any finite dimensional basic associative algebra, we study the presentation spaces and their relation to 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.

[发布机构] University of Michigan

[效力级别] Non-commutative Algebra

[关键词] Representation Theory;Non-commutative Algebra;General Representation;Projective Presentation;Canonical Decomposition;Quiver;Mathematics;Science;Mathematics