The structure of AR-quivers and matrix bimodule problems

Abstract

We introduce briefly the following contents on representation of Artin algebras:the structure of stable components of AR-quivers; the property of stable components of wild hereditary algebras;the matrix bimodule problems introduced by finitely dimensional algebras over an algebraically closed field,the dual co-bimodule problems, and associated boxes; almost one-by-one correspondence of almost split sequences betweenrepresentation categories of mod$\Lambda$, $P_1(\Lambda)$ and associated box; the dimension and property ofHom-spaces of any two modules over an tame algebra $\Lambda$. We also give a brief introduction to the tameness and homogeneousproperty of Artin algebras.