Homotopy category of N-complexes of projective modules

2015/04/04 by Bahiraei, Payam, Hafezi, Rasool, Nematbakhsh, Amin
#16G99 #18E30 #18G05 #18G35 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1504.01043

Abstract

In this paper, we show that the homotopy category of N-complexes of projective R-modules is triangle equivalent to the homotopy category of projective T_N-1(R)- modules where T_N-1(R) is the ring of triangular matrices of order N-1 with entries in R. We also define the notions of N-singularity category and N-totally acyclic complexes. We show that the category of N-totally acyclic complexes of finitely generated projective R-modules embeds in the N-singularity category, which is a result analogous to the case of ordinary chain complexes.

Related

• The homotopy category of acyclic complexes of pure-projective modules
• The homotopy category of complexes of projective modules
• Complete intersections and equivalences with categories of matrix factorizations
• Structures on the Category of N-Complexes
• The homotopy category of N-complexes is a homotopy category