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On the type of a category of complexes of fixed size and the strong global dimension

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Abstract

We prove that if the strong global dimension η of an algebra A is finite, then Cη+ 1(proj A) is of finite type if and only if for each n ≥ 2, Cn(projA) is of finite type. Moreover, we also prove some implications in order to know if for some positive integer is Cn(projA) of infinite type. We determine the strong global dimension of some piecewise hereditary finite dimensional algebras taking into account their ordinary quivers with relations.

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Acknowledgments

All authors thankfully acknowledge partial support from CONICET and from Universidad Nacional de Mar del Plata, Argentina. The first author is a researcher from CONICET.

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Authors and Affiliations

  1. Centro Marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y Naturales, Funes 3350, Universidad Nacional de Mar del Plata and CONICET, Mar del Plata, 7600, Argentina

    Claudia Chaio

  2. Centro Marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y Naturales, Funes 3350, Universidad Nacional de Mar del Plata, Mar del Plata, 7600, Argentina

    Alfredo González Chaio & Isabel Pratti

Authors
  1. Claudia Chaio
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  2. Alfredo González Chaio
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  3. Isabel Pratti
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Correspondence to Claudia Chaio.

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Presented by: Michel Van den Bergh

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Chaio, C., González Chaio, A. & Pratti, I. On the type of a category of complexes of fixed size and the strong global dimension. Algebr Represent Theor 22, 1343–1370 (2019). https://doi.org/10.1007/s10468-018-9823-3

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  • DOI: https://doi.org/10.1007/s10468-018-9823-3

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