作为衡量Artin 代数与有限表示型代数距离的方法, Artin 代数的表示维数一直是代数表示论中热门的研究对象. 它不仅是一个重要的同调不变量, 而且与同调代数中的有限维猜想密切联系. 本项目通过对某些特殊模类性质的研究, 利用逼近理论和导出维数来研究包括Auslander正则代数、Auslander-Gorenstein代数在内的Auslander-型代数及其扩张( 例如优化扩张, Frobenius扩张, 单点扩张)的表示维数. 力求为包括有限维数猜想在内的一些同调猜想的最终解决提供理论支持.

As a way of measuring how far an Artin algebra is from being of finite representation type, the representation dimension of an Artin algebra is a hot research object in representation theory of algebra. It is not only an important homological invariant, but also closely related with finitistic dimension conjecture. In this project, by studyng the properties of some special categories of modules, we will study the representation dimension of Auslander-type algebras including Auslander regular algebras and Auslander-Gorenstein algebras and their some extensions (e.g. excellent extensions, Frobenius extensions, one-point extensions) by means of appromation theory and derived dimension. And we try to provide theoretical support to the finial solution of some homological conjectures including finitistic dimension conjecture.