2021/09/16 by Brightbill, Jeremy R. B., Miemietz, Vanessa
#16E35 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2109.07728
A well-known theorem of Buchweitz provides equivalences between three categories: the stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy category of acyclic complexes of projectives, and the singularity category. To adapt this result to N-complexes, one must find an appropriate candidate for the N-analogue of the stable category. We identify this "N-stable category" via the monomorphism category and prove Buchweitz's theorem for N-complexes over a Frobenius exact abelian category. We also compute the Serre functor on the N-stable category over a self-injective algebra and study the resultant fractional Calabi-Yau properties.