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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Autores principales: Cibils, C., Solotar, A., Wisbauer, R.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00103616_v272_n3_p837_Cibils
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00103616_v272_n3_p837_Cibils2023-10-03T14:09:01Z N-complexes as functors, amplitude cohomology and fusion rules Cibils, C. Solotar, A. Wisbauer, R. 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. Fil:Solotar, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00103616_v272_n3_p837_Cibils
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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.
format JOUR
author Cibils, C.
Solotar, A.
Wisbauer, R.
spellingShingle Cibils, C.
Solotar, A.
Wisbauer, R.
N-complexes as functors, amplitude cohomology and fusion rules
author_facet Cibils, C.
Solotar, A.
Wisbauer, R.
author_sort Cibils, C.
title N-complexes as functors, amplitude cohomology and fusion rules
title_short N-complexes as functors, amplitude cohomology and fusion rules
title_full N-complexes as functors, amplitude cohomology and fusion rules
title_fullStr N-complexes as functors, amplitude cohomology and fusion rules
title_full_unstemmed N-complexes as functors, amplitude cohomology and fusion rules
title_sort n-complexes as functors, amplitude cohomology and fusion rules
url http://hdl.handle.net/20.500.12110/paper_00103616_v272_n3_p837_Cibils
work_keys_str_mv AT cibilsc ncomplexesasfunctorsamplitudecohomologyandfusionrules
AT solotara ncomplexesasfunctorsamplitudecohomologyandfusionrules
AT wisbauerr ncomplexesasfunctorsamplitudecohomologyandfusionrules
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