Degenerations and Stable Homomorphisms^#

^#Communicated by C. Cibils.

Let Λ be an algebra over an algebraically closed field. We compare the partial order ≤ _hom in the module category of Λ with a certain relation ≤ _stab in the stable module category of Λ. Both relations coincide if Λ is hereditary. Starting with any non-hereditary representation-finite algebra Λ, we construct a representation-finite algebra Λ′, obtained by a covering of the Auslander-Reiten quiver of Λ, such that for Λ′ both relations do not coincide.

Key Words:

• Coverings
• Degenerations
• Representation-theory of finite dimensional algebras
• Stable module category

Notes

^#Communicated by C. Cibils.