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Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor

Published online by Cambridge University Press:  20 November 2018

Javad Asadollahi
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran and School of Mathematics, Institute for Research in Fundamental Science (IPM), Tehran, Iran. e-mail: asadollahi@ipm.ir. vahed@ipm.ir. hafezi@ipm.ir
Rasool Hafezi
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran and School of Mathematics, Institute for Research in Fundamental Science (IPM), Tehran, Iran. e-mail: asadollahi@ipm.ir. vahed@ipm.ir. hafezi@ipm.ir
Razieh Vahed
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran and School of Mathematics, Institute for Research in Fundamental Science (IPM), Tehran, Iran. e-mail: asadollahi@ipm.ir. vahed@ipm.ir. hafezi@ipm.ir
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Abstract

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We study bounded derived categories of the category of representations of infinite quivers over a ring $R$. In case $R$ is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left (resp. right) rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2015

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