arXiv math/06055692006-05math.QAmath.RT

N-complexes as functors, amplitude cohomology and fusion rules

Claude Cibils, Andrea Solotar, Robert Wisbauer

备注：: Final version
发表信息：: Communications in Mathematical Physics 272, 3 (05/03/2007) 837--649
DOI：: 10.1007/s00220-007-0210-x

英文摘要：

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.

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