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Algebras and Representation Theory

, Volume 22, Issue 6, pp 1343–1370 | Cite as

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

  • Claudia ChaioEmail author
  • Alfredo González Chaio
  • Isabel Pratti
Article
  • 49 Downloads

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.

Keywords

Complexes Projective Strong global dimension Derived bounded category Degrees 

Mathematics Subject Classification (2010)

16G70 16G20 16E10 

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Notes

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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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Claudia Chaio
    • 1
    Email author
  • Alfredo González Chaio
    • 2
  • Isabel Pratti
    • 2
  1. 1.Centro Marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y Naturales, Funes 3350Universidad Nacional de Mar del Plata and CONICETMar del PlataArgentina
  2. 2.Centro Marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y Naturales, Funes 3350Universidad Nacional de Mar del PlataMar del PlataArgentina

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