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Publication Date:
May 2010
ISSN:
1435-5337
DOI:
10.1515/form.2011.044

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Combinatorial classification of piecewise hereditary algebras

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1Centro de Matemática (CMAT), Instituto de Matemática y Estadística Rafael Laguardia (IMERL), Universidad de la República, Iguá 4225, C.P. 11400, Montevideo, Uruguay.

2Instituto de Matemática, Universidad Nacional del Sur, Av. Alem 1253, (8000) Bahía Blanca, Argentina.

3Université de Lyon, 42023, Saint-Etienne, France.

4Université de Saint-Etienne, Jean Monnet, 42023, Saint-Etienne, France.

5LaMUSE, EA3989, 42023, Saint-Etienne, France.

Citation Information: Forum Mathematicum. Volume 23, Issue 6, Pages 1203–1215, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/form.2011.044, May 2010

Publication History:
Received:
2009-03-25
Published Online:
2010-05-31

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.

Keywords.: Piecewise hereditary algebra; Coxeter polynomial

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