2025/03/06 by Ioannis Emmanouil, Wei Ren, Emmanouil, Ioannis +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2503.04284
In this paper, we examine the class of cofibrant modules over a group algebra kG, that were defined by Benson in [2]. We show that this class is always the left-hand side of a complete hereditary cotorsion pair in the category of kG-modules. It follows that the class of Gorenstein projective kG-modules is special precovering in the category of kG-modules, if G is contained in the class \scriptstyle\bf LH\mathfrakF of hierarchically decomposable groups defined by Kropholler in [20] and k has finite weak global dimension. It also follows that the obstruction to the equality between the classes of cofibrant and Gorenstein projective kG-modules can be described, over any group algebra kG, in terms of a suitable subcategory of the stable category of Gorenstein projective kG-modules.