Combinatorial classification of piecewise hereditary algebras

2009/03/25 by Marcelo Lanzilotta, Lanzilotta, Marcelo, Maria Julia Redondo +3
Mathematics · #15A15 #16E60 #16S99. #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:15A15 #msc:16E60 #msc:16S99.

paper · pdf · doi:10.48550/arxiv.0903.4326

arxiv created 2009/03/25 · arxiv updated 2009/12/01

Abstract

We use the characteristic polynomial of the Coxeter matrix of an algebra to complete the combinatorial classification of piecewise hereditary algebras which Happel gave in terms of the trace of the Coxeter matrix. We also give a cohomological interpretation of the coefficients (other than the trace) of the characteristic polynomial of the Coxeter matrix of any finite dimensional algebra with finite global dimension.

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