Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras

Abstract

Gorenstein-projective module is an important research topic in relative homological algebra, representation theory of algebras, triangulated categories, and algebraic geometry (especially in singularity theory). For a given algebra A, how to construct all the Gorenstein-projective A-modules is a fundamental problem in Gorenstein homological algebra. In this paper, we describe all complete projective resolutions over an upper triangular Artin algebra Λ=AMBA0B. We also give a necessary and sufficient condition for all finitely generated Gorenstein-projective modules over Λ=AMBA0B.