2017/09/04 by René Marczinzik, Marczinzik, Rene · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1709.01132
In \citeAB, Auslander and Bridger introduced Gorenstein projective modules and only about 40 years after their introduction a finite dimensional algebra A was found in \citeJS where the subcategory of Gorenstein projective modules did not coincide with ⊥A, the category of stable modules. The example in \citeJS is a commutative local algebra. We explain why it is of interest to find such algebras that are non-local with regard to the homological conjectures. We then give a first systematic construction of algebras where the subcategory of Gorenstein projective modules does not coincide with ⊥A using the theory of gendo-symmetric algebras. We use Liu-Schulz algebras to show that our construction works to give examples of such non-local algebras with an arbitrary number of simple modules.