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On global cohomological width of artin algebras

Volume 146 / 2017

Chao Zhang Colloquium Mathematicum 146 (2017), 31-46 MSC: Primary 16E10; Secondary 16G10, 18E30. DOI: 10.4064/cm6714-10-2015 Published online: 15 July 2016

Abstract

We study the global cohomological width of artin algebras. Using the construction of indecomposable objects in the triangulated category via taking cones due to Happel and Zacharia (2008), we establish that global cohomological width coincides with strong global dimension. Moreover, an upper bound for the global cohomological width of piecewise hereditary algebras is obtained. As an application, we construct finite-dimensional piecewise hereditary algebras of type $\mathbb {A}$ and $\mathbb {D}$ with global cohomological width an arbitrary positive integer $m$. Finally, we find a relation between recollements and global cohomological width.

Authors

  • Chao ZhangDepartment of Mathematics
    Guizhou University
    Guiyang 550025, P.R. China
    and
    Faculty of Mathematics
    Bielefeld University
    33501 Bielefeld, Germany
    e-mail

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