2015/09/11 by Chávez, Alfredo Nájera
#16G20 #18G35 #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1509.03686
Let \mathcal E be a Frobenius category, \mathcal P its subcategory of projective objects and F:\mathcal E → \mathcal E an exact automorphism. We prove that there is a fully faithful functor from the orbit category \mathcal E/F into gpr(\mathcal P/F), the category of finitely-generated Gorenstein-projective modules over \mathcal P/F. We give sufficient conditions to ensure that the essential image of \mathcal E/F is an extension-closed subcategory of gpr(\mathcal P/F). If \mathcal E is in addition Krull-Schmidt, we give sufficient conditions to ensure that the completed orbit category \mathcal E \widehat / F is a Krull-Schmidt Frobenius category. Finally, we apply our results on completed orbit categories to the context of Nakajima categories associated to Dynkin quivers and sketch applications to cluster algebras.