The notion of N-complexes goes back to a 1996 preprint of Kapranov, in which he considered chains of composable morphisms satisfying d^N = 0 (as opposed to the usual $d^2 = 0$ which gives the usual chain complexes). Later on, much of the usual homological algebra for chain complexes (homotopy of morphisms, spectral sequences, etc) was generalized to N-complexes, mostly by Dubois-Violette. Recently in 2014 there has been a burst of interest in this topic with work of Iyama,Kato,Miyachi defining the corresponding N-derived category. We shall begin the talk with simple definitions of $N$ complexes and their homology groups. Then gradually we will move to the paper of Iyama explaining derived category of $N$-complexes.

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Last updated: 15 Apr 2024