General Presentations of Algebras.

Representation Theory;Non-commutative Algebra;General Representation;Projective Presentation;Canonical Decomposition;Quiver;Mathematics;Science;Mathematics

Fei, JiaruiPando Zayas, Leopoldo A. ;

University of Michigan

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

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/77740/jiarui_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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.