连通分次代数上投射模范畴的三角结构

Triangulated Structure of the Category of Projective Modules on the Connected Graded Algebra

首先将一般的Quasi-Frobenius环的刻画推广到分次Quasi-Frobenius环上.接下来,给出了投射模范畴有三角结构的连通分次代数的一个刻画.反之,当连通分次代数满足一定条件时,给出了投射模范畴的三角结构,并证明了这些三角结构全体和k中非零元素全体之间的一一对应关系.最后,证明了具有不同三角结构的投射模范畴作为三角范畴是等价的.

Firstly, it characterizes the graded Quasi-Frobenius ring, then it also characterizes the connected graded algebra, for which the category of projective modules admits a triangulation. Conversely, under some assumptions on the connected graded algebra, a triangulated structure for the category of projective modules was constructed. Besides, there is a one to one correspondence between the set of all the triangulated structures of the category of projective modules and the set of nonzero elements in k. Finally, it was proved that the categories, of projective modules, with different triangulated structure are triangulated equivalent.