AR-箭图的构造和矩阵双模问题

The structure of AR-quivers and matrix bimodule problems

本文简要介绍了Artin代数表示理论中的下述内容:Auslander-Reiten箭图(简称AR-箭图)稳定分支的结构,野型遗传代数稳定分支的性质,代数闭域上有限维代数Λ引出的矩阵双模问题、对偶的余双模问题及其相伴的具有余代数结构的双模(简称box), modΛ、P_1(Λ)及相伴box的表示范畴之间几乎可列序列的几乎一一对应,驯顺代数Λ上任意两个模之间态射集的维数和性质;最后介绍了代数的驯顺性与其模范畴的齐性.

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 cobimodule problems, and associated boxes; almost one-by-one correspondence of almost split sequences between representation categories of modΛ, P_1（Λ） and associated box; the dimension and property of Hom-spaces of any two modules over an tame algebra Λ. We also give a brief introduction to the tameness and homogeneous property of Artin algebras.