m-重代数A^((m))上的倾斜模

Tilting modules over m-replicated algebra A^((m))

设A是代数闭域k上的有限维遗传代数,A^((m))和ζ_m(A)分别是A的m-重代数和m-丛范畴.众所周知,代数A^((m))的投射维数不超过m的基本的(basic)倾斜模与m-丛范畴ζ_m(A)的基本的倾斜对象一一对应,这是本文进一步研究m-重代数的倾斜模的原因.本文综述m-重代数A^((m))的偏倾斜模的补、倾斜箭图、倾斜模的自同态代数以及生成子-余生成子的自同态代数的整体维数的值分布.

Let A be a finite dimensional hereditary algebra over an algebraically closed field k,A^（（m））and ζ_m（A）be the m-replicated algebra and the m-cluster category of A respectively.It is well known that there is a oneto-one correspondence between basic tilting A^（（m））-modules with projective dimension at most m and basic tilting objects in m-cluster category ζ_m（A）.This motivates the further investigation on the tilting modules over mreplicated algebras.In this paper,we review some results of our research on the complements of partial tilting A^（（m））-modules,the tilting quivers of A^（（m））,the endomorphism algebras of tilting A^（（m））-modules and the values of global dimensions of the endomorphism algebras of generator-cogenerators over A^（（m））.