2006/05/31 by Claude Cibils, Andrea Solotar, Robert Wisbauer · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.QA #math.RT #msc:16E05 #msc:16W50 #msc:18E10
paper · pdf · doi:10.1007/s00220-007-0210-x
published as Communications in Mathematical Physics 272, 3 (05/03/2007) 837--649 · Final version
arxiv created 2006/10/01 · openalex publication_date 2007/03/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only vanishes on injective functors providing a well defined functor on the stable category. For left truncated N-complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive N-complexes is proved to be isomorphic to an Ext functor of an indecomposable N-complex inside the abelian functor category. Finally we show that for the monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other words the fusion rules for N-complexes can be determined.