morphisms between bound quivers
Let and be bound quivers (http://planetmath.org/AdmissibleIdealsBoundQuiverAndItsAlgebra) over the same base field .
Definition. A morphism is said to be bounded by if the induced linear map (http://planetmath.org/MorphismsOfPathAlgebrasInducedFromMorphismsOfQuivers) is such that
In this case we write
and we say that is a morphism of bound quivers.
If is a morphism of bound quivers, then induces a linear map
Furthermore, if is injective, then is a homomorphism of algebras (see this entry (http://planetmath.org/MorphismsOfPathAlgebrasInducedFromMorphismsOfQuivers) for details) and thus is a homormorphism of algebras.
|Title||morphisms between bound quivers|
|Date of creation||2013-03-22 19:17:07|
|Last modified on||2013-03-22 19:17:07|
|Last modified by||joking (16130)|