Monic representations and Gorenstein-projective modules
Luo, Xiu-Hua ; Zhang, Pu
arXiv, 1110.6021 / Harvested from arXiv
Text on arXiv
Let $\Lambda$ be the path algebra of a finite quiver $Q$ over a finite-dimensional algebra $A$. Then $\Lambda$-modules are identified with representations of $Q$ over $A$. This yields the notion of monic representations of $Q$ over $A$. If $Q$ is acyclic, then the Gorenstein-projective $\m$-modules can be explicitly determined via the monic representations. As an application, $A$ is self-injective if and only if the Gorenstein-projective $\m$-modules are exactly the monic representations of $Q$ over $A$.
Publié le : 2011-10-27
Classification:  Mathematics - Representation Theory,  Mathematics - Rings and Algebras,  16G10, 16E65, 16G50, 16G60 
@article{1110.6021,
     author = {Luo, Xiu-Hua and Zhang, Pu},
     title = {Monic representations and Gorenstein-projective modules},
     journal = {arXiv},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1110.6021}
}

Luo, Xiu-Hua; Zhang, Pu. Monic representations and Gorenstein-projective modules. arXiv, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/1110.6021/