N-complexes as functors, amplitude cohomology and fusion rules
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 (called generalized cohomology by M. Dubois-Violette) only vanishes on injective functors providing a well defined functor on t...
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2007
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00103616_v272_n3_p837_Cibils http://hdl.handle.net/20.500.12110/paper_00103616_v272_n3_p837_Cibils |
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| Sumario: | 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 (called generalized cohomology by M. Dubois-Violette) 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. © Springer-Verlag 2007. |
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