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ON HOMOLOGICAL FROBENIUS COMPLEXES AND BIMODULES

Published online by Cambridge University Press:  22 August 2014

J. R. GARCÍA ROZAS ,
LUIS OYONARTE  and
BLAS TORRECILLAS
J. R. GARCÍA ROZAS
Affiliation:
Departamento de Matemáticas, Universidad de Almería, 04071 Almería, Spain e-mails: jrgrozas@ual.es, oyonarte@ual.es, btorreci@ual.es
LUIS OYONARTE
Affiliation:
Departamento de Matemáticas, Universidad de Almería, 04071 Almería, Spain e-mails: jrgrozas@ual.es, oyonarte@ual.es, btorreci@ual.es
BLAS TORRECILLAS
Affiliation:
Departamento de Matemáticas, Universidad de Almería, 04071 Almería, Spain e-mails: jrgrozas@ual.es, oyonarte@ual.es, btorreci@ual.es
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Abstract

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We introduce the concept of homological Frobenius functors as the natural generalization of Frobenius functors in the setting of triangulated categories, and study their structure in the particular case of the derived categories of those of complexes and modules over a unital associative ring. Tilting complexes (modules) are examples of homological Frobenius complexes (modules). Homological Frobenius functors retain some of the nice properties of Frobenius ones as the ascent theorem for Gorenstein categories. It is shown that homological Frobenius ring homomorphisms are always Frobenius.

Keywords

Primary 16E65Secondary 18E30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 3 , September 2014 , pp. 629 - 642
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

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