Monic representations and Gorenstein-projective modules

By Xiu-Hua Luo, Pu Zhang. 2011

72 citations recorded by the source corpus.

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 $A$.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4805e84aaefc67974062e5005495f1755429cfe2

Citations in the corpus

• Representations of quivers over the algebra of dual numbers (2011, unknown): “In a recent paper Luo and Zhang [LZ] gave a characterization of the Gorenstein-projective AQ-modules, where Q is a finite directed quiver and A a any k-algebra, thus one may try to use this result in order to construct these modules explicitly.”