morphisms between bound quivers

Let (Q,I) and (Q,I) be bound quivers ( over the same base fieldMathworldPlanetmath k.

Definition. A morphism F:QQ is said to be bounded by (I,I) if the induced linear map ( F¯:kQkQ is such that


In this case we write


and we say that F is a morphism of bound quivers.

If F:(Q,I)(Q,I) is a morphism of bound quivers, then F¯:kQkQ induces a linear map


Furthermore, if F0 is injective, then F¯ is a homomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath of algebras (see this entry ( for details) and thus F¯¯ is a homormorphism of algebras.

Title morphisms between bound quivers
Canonical name MorphismsBetweenBoundQuivers
Date of creation 2013-03-22 19:17:07
Last modified on 2013-03-22 19:17:07
Owner joking (16130)
Last modified by joking (16130)
Numerical id 5
Author joking (16130)
Entry type Definition
Classification msc 14L24